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Evaluating algebraic expressions, example 8: describing algebraic expressions.

  • [latex]\frac{4}{3}\pi {r}^{3}[/latex]
  • [latex]\sqrt{2{m}^{3}{n}^{2}}[/latex]
  • [latex]2\pi r\left(r+h\right)[/latex]
  • [latex]4{y}^{3}+y[/latex]

Example 9: Evaluating an Algebraic Expression at Different Values

  • [latex]x=0[/latex]
  • [latex]x=1[/latex]
  • [latex]x=\frac{1}{2}[/latex]
  • [latex]x=-4[/latex]
  • Substitute 0 for [latex]x[/latex]. [latex]\begin{array}\text{ }2x-7 \hfill& = 2\left(0\right)-7 \\ \hfill& =0-7 \\ \hfill& =-7\end{array}[/latex]
  • Substitute 1 for [latex]x[/latex]. [latex]\begin{array}\text{ }2x-7 \hfill& = 2\left(1\right)-7 \\ \hfill& =2-7 \\ \hfill& =-5\end{array}[/latex]
  • Substitute [latex]\frac{1}{2}[/latex] for [latex]x[/latex]. [latex]\begin{array}\text{ }2x-7 \hfill& = 2\left(\frac{1}{2}\right)-7 \\ \hfill& =1-7 \\ \hfill& =-6\end{array}[/latex]
  • Substitute [latex]-4[/latex] for [latex]x[/latex]. [latex]\begin{array}\text{ }2x-7 \hfill& = 2\left(-4\right)-7 \\ \hfill& =-8-7 \\ \hfill& =-15\end{array}[/latex]

a. [latex]y=2[/latex] b. [latex]y=0[/latex] c. [latex]y=\frac{2}{3}[/latex] d. [latex]y=-5[/latex]

Example 10: Evaluating Algebraic Expressions

  • [latex]x+5[/latex] for [latex]x=-5[/latex]
  • [latex]\frac{t}{2t - 1}\\[/latex] for [latex]t=10[/latex]
  • [latex]\frac{4}{3}\pi {r}^{3}\\[/latex] for [latex]r=5[/latex]
  • [latex]a+ab+b[/latex] for [latex]a=11,b=-8[/latex]
  • [latex]\sqrt{2{m}^{3}{n}^{2}}[/latex] for [latex]m=2,n=3[/latex]
  • Substitute [latex]-5[/latex] for [latex]x[/latex]. [latex]\begin{array}\text{ }x+5\hfill&=\left(-5\right)+5 \\ \hfill&=0\end{array}[/latex]
  • Substitute 10 for [latex]t[/latex]. [latex]\begin{array}\text{ }\frac{t}{2t-1}\hfill& =\frac{\left(10\right)}{2\left(10\right)-1} \\ \hfill& =\frac{10}{20-1} \\ \hfill& =\frac{10}{19}\end{array}[/latex]
  • Substitute 5 for [latex]r[/latex]. [latex]\begin{array}\text{ }\frac{4}{3}\pi r^{3} \hfill& =\frac{4}{3}\pi\left(5\right)^{3} \\ \hfill& =\frac{4}{3}\pi\left(125\right) \\ \hfill& =\frac{500}{3}\pi\end{array}[/latex]
  • Substitute 11 for [latex]a[/latex] and –8 for [latex]b[/latex]. [latex]\begin{array}\text{ }a+ab+b \hfill& =\left(11\right)+\left(11\right)\left(-8\right)+\left(-8\right) \\ \hfill& =11-8-8 \\ \hfill& =-85\end{array}[/latex]
  • Substitute 2 for [latex]m[/latex] and 3 for [latex]n[/latex]. [latex]\begin{array}\text{ }\sqrt{2m^{3}n^{2}} \hfill& =\sqrt{2\left(2\right)^{3}\left(3\right)^{2}} \\ \hfill& =\sqrt{2\left(8\right)\left(9\right)} \\ \hfill& =\sqrt{144} \\ \hfill& =12\end{array}[/latex]

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2.3: Evaluate, Simplify, and Translate Expressions (Part 1)

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Learning Objectives

  • Evaluate algebraic expressions
  • Identify terms, coefficients, and like terms
  • Simplify expressions by combining like terms
  • Translate word phrases to algebraic expressions

Be prepared!

Before you get started, take this readiness quiz.

  • Is \(n ÷ 5\) an expression or an equation? If you missed this problem, review Example 2.1.4 .
  • Simplify \(4^5\). If you missed this problem, review Example 2.1.6 .
  • Simplify \(1 + 8 • 9\). If you missed this problem, review Example 2.1.8 .

Evaluate Algebraic Expressions

In the last section, we simplified expressions using the order of operations. In this section, we’ll evaluate expressions—again following the order of operations.

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.

Example \(\PageIndex{1}\): evaluate

Evaluate \(x + 7\) when

  • To evaluate, substitute \(3\) for \(x\) in the expression, and then simplify.

When \(x = 3\), the expression \(x + 7\) has a value of \(10\).

  • To evaluate, substitute \(12\) for \(x\) in the expression, and then simplify.

When \(x = 12\), the expression \(x + 7\) has a value of \(19\). Notice that we got different results for parts (a) and (b) even though we started with the same expression. This is because the values used for \(x\) were different. When we evaluate an expression, the value varies depending on the value used for the variable.

exercise \(\PageIndex{1}\)

Evaluate: \(y + 4\) when

exercise \(\PageIndex{2}\)

Evaluate: \(a − 5\) when

Example \(\PageIndex{2}\)

Evaluate \(9x − 2\), when

Remember \(ab\) means \(a\) times \(b\), so \(9x\) means \(9\) times \(x\).

  • To evaluate the expression when \(x = 5\), we substitute \(5\) for \(x\), and then simplify.
  • To evaluate the expression when \(x = 1\), we substitute \(1\) for \(x\), and then simplify.

Notice that in part (a) that we wrote \(9 • 5\) and in part (b) we wrote \(9(1)\). Both the dot and the parentheses tell us to multiply.

exercise \(\PageIndex{3}\)

Evaluate: \(8x − 3\), when

exercise \(\PageIndex{4}\)

Evaluate: \(4y − 4\), when

Example \(\PageIndex{3}\): evaluate

Evaluate \(x^2\) when \(x = 10\).

We substitute \(10\) for \(x\), and then simplify the expression.

When \(x = 10\), the expression \(x^2\) has a value of \(100\).

exercise \(\PageIndex{5}\)

Evaluate: \(x^2\) when \(x = 8\).

exercise \(\PageIndex{6}\)

Evaluate: \(x^3\) when \(x = 6\).

Example \(\PageIndex{4}\): evaluate

Evaluate \(2^x\) when \(x = 5\).

In this expression, the variable is an exponent.

When \(x = 5\), the expression \(2^x\) has a value of \(32\).

exercise \(\PageIndex{7}\)

Evaluate: \(2^x\) when \(x = 6\).

exercise \(\PageIndex{8}\)

Evaluate: \(3^x\) when \(x = 4\).

Example \(\PageIndex{5}\): evaluate

Evaluate \(3x + 4y − 6\) when \(x = 10\) and \(y = 2\).

This expression contains two variables, so we must make two substitutions.

When \(x = 10\) and \(y = 2\), the expression \(3x + 4y − 6\) has a value of \(32\).

exercise \(\PageIndex{9}\)

Evaluate: \(2x + 5y − 4\) when \(x = 11\) and \(y = 3\)

exercise \(\PageIndex{10}\)

Evaluate: \(5x − 2y − 9\) when \(x = 7\) and \(y = 8\)

Example \(\PageIndex{6}\): evaluate

Evaluate \(2x^2 + 3x + 8\) when \(x = 4\).

We need to be careful when an expression has a variable with an exponent. In this expression, \(2x^2\) means \(2 • x • x\) and is different from the expression \((2x)^2\), which means \(2x • 2x\).

exercise \(\PageIndex{11}\)

Evaluate: \(3x^2 + 4x + 1\) when \(x = 3\).

exercise \(\PageIndex{12}\)

Evaluate: \(6x^2 − 4x − 7\) when \(x = 2\).

Identify Terms, Coefficients, and Like Terms

Algebraic expressions are made up of terms . A term is a constant or the product of a constant and one or more variables. Some examples of terms are \(7\), \(y\), \(5x^2\), \(9a\), and \(13xy\).

The constant that multiplies the variable(s) in a term is called the coefficient . We can think of the coefficient as the number in front of the variable. The coefficient of the term \(3x\) is \(3\). When we write \(x\), the coefficient is \(1\), since \(x = 1 • x\). Table \(\PageIndex{1}\) gives the coefficients for each of the terms in the left column.

An algebraic expression may consist of one or more terms added or subtracted. In this chapter, we will only work with terms that are added together. Table \(\PageIndex{2}\) gives some examples of algebraic expressions with various numbers of terms. Notice that we include the operation before a term with it.

Example \(\PageIndex{7}\):

Identify each term in the expression \(9b + 15x^2 + a + 6\). Then identify the coefficient of each term.

The expression has four terms. They are \(9b\), \(15x^2\), \(a\), and \(6\).

The coefficient of \(9b\) is \(9\).

The coefficient of \(15x^2\) is \(15\).

Remember that if no number is written before a variable, the coefficient is \(1\). So the coefficient of a is \(1\).

The coefficient of a constant is the constant, so the coefficient of \(6\) is \(6\).

exercise \(\PageIndex{13}\)

Identify all terms in the given expression, and their coefficients: \(4x + 3b + 2\)

The terms are \(4x, 3b,\) and \(2\). The coefficients are \(4, 3,\) and \(2\).

exercise \(\PageIndex{14}\)

Identify all terms in the given expression, and their coefficients: \(9a + 13a^2 + a^3\)

The terms are \(9a, 13a^2,\) and \(a^3\), The coefficients are \(9, 13,\) and \(1\).

Some terms share common traits. Look at the following terms. Which ones seem to have traits in common?

\(5x, 7, n^{2}, 4, 3x, 9n^{2}\)

Which of these terms are like terms?

  • The terms \(7\) and \(4\) are both constant terms.
  • The terms \(5x\) and \(3x\) are both terms with \(x\).
  • The terms \(n^2\) and \(9n^2\) both have \(n^2\).

Terms are called like terms if they have the same variables and exponents. All constant terms are also like terms. So among the terms \(5x, 7, n^2, 4, 3x, 9n^2, 7\) and \(4\) are like terms, \(5x\) and \(3x\) are like terms, and \(n^2\) and \(9n^2\) are like terms.

Definition: Like terms

Terms that are either constants or have the same variables with the same exponents are like terms.

Example \(\PageIndex{8}\): identify

Identify the like terms:

  • \(y^3, 7x^2, 14, 23, 4y^3, 9x, 5x^2\)
  • \(4x^2 + 2x + 5x^2 + 6x + 40x + 8xy\)

Look at the variables and exponents. The expression contains \(y^3, x^2, x\), and constants. The terms \(y^3\) and \(4y^3\) are like terms because they both have \(y^3\). The terms \(7x^2\) and \(5x^2\) are like terms because they both have \(x^2\). The terms \(14\) and \(23\) are like terms because they are both constants. The term \(9x\) does not have any like terms in this list since no other terms have the variable \(x\) raised to the power of \(1\).

Look at the variables and exponents. The expression contains the terms \(4x^2, 2x, 5x^2, 6x, 40x\), and \(8xy\) The terms \(4x^2\) and \(5x^2\) are like terms because they both have \(x^2\). The terms \(2x, 6x\), and \(40x\) are like terms because they all have \(x\). The term \(8xy\) has no like terms in the given expression because no other terms contain the two variables \(xy\).

exercise \(\PageIndex{15}\)

Identify the like terms in the list or the expression: \(9, 2x^3, y^2, 8x^3, 15, 9y, 11y^2\)

\(9, 15\); \(2x^3\) and \(8x^3\), \(y^2\), and \(11y^2\)

exercise \(\PageIndex{16}\)

Identify the like terms in the list or the expression: \(4x^3 + 8x^2 + 19 + 3x^2 + 24 + 6x^3\)

\(4x^3\) and \(6x^3\); \(8x^2\) and \(3x^2\); \(19\) and \(24\)

Simplify Expressions by Combining Like Terms

We can simplify an expression by combining the like terms. What do you think \(3x + 6x\) would simplify to? If you thought \(9x\), you would be right!

We can see why this works by writing both terms as addition problems.

CNX_BMath_Figure_02_02_001_img.jpg

Add the coefficients and keep the same variable. It doesn’t matter what \(x\) is. If you have \(3\) of something and add \(6\) more of the same thing, the result is \(9\) of them. For example, \(3\) oranges plus \(6\) oranges is \(9\) oranges. We will discuss the mathematical properties behind this later.

The expression \(3x + 6x\) has only two terms. When an expression contains more terms, it may be helpful to rearrange the terms so that like terms are together. The Commutative Property of Addition says that we can change the order of addends without changing the sum. So we could rearrange the following expression before combining like terms.

CNX_BMath_Figure_02_02_015_img.jpg

Now it is easier to see the like terms to be combined.

HOW TO: COMBINE LIKE TERMS

Step 1. Identify like terms.

Step 2. Rearrange the expression so like terms are together.

Step 3. Add the coefficients of the like terms.

Example \(\PageIndex{9}\): simplify

Simplify the expression: \(3x + 7 + 4x + 5\).

exercise \(\PageIndex{17}\)

Simplify: \(7x + 9 + 9x + 8\)

exercise \(\PageIndex{18}\)

Simplify: \(5y + 2 + 8y + 4y + 5\)

Example \(\PageIndex{10}\): simplify

Simplify the expression: \(7x^2 + 8x + x^2 + 4x\).

These are not like terms and cannot be combined. So \(8x^2 + 12x\) is in simplest form.

exercise \(\PageIndex{19}\)

Simplify: \(3x^2 + 9x + x^2 + 5x\)

\(4x^2+14x\)

exercise \(\PageIndex{20}\)

Simplify: \(11y^2 + 8y + y^2 + 7y\)

\(12y^2+15y\)

Contributors and Attributions

  • Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (formerly of Santa Ana College). This content produced by OpenStax and is licensed under a  Creative Commons Attribution License 4.0  license.

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Are You Ready to Evaluate Algebraic Expressions?

In the past, you've evaluated numerical expressions by using the order of operations . We are going to use these same rules to evaluate algebraic expressions .

What is an Algebraic Expression?

An Algebraic expression is an expression that you will see most often once you start Algebra. In Algebra we work with variables and numerals.

A variable is a symbol, usually a letter, that represents one or more numbers.

Thus, an algebraic expression consists of numbers, variables, and operations.

Examples of Algebraic Expressions

An algebraic expression consists of numbers, variables, and operations. Here are a few examples:

algebra 1 assignment evaluate each using the values given

In order to evaluate an algebraic expression, you must know the exact values for each variable. Then you will simply substitute and evaluate using the order of operations . Take a look at example 1.

Example 1 - Evaluating Algebraic Expressions

algebra 1 assignment evaluate each using the values given

Now, lets evaluate algebraic expressions with more than one variable. Don't forget to always use the order of operations when evaluating the expression after substituting.

Example 2 - Expressions with More Than One      Variable

algebra 1 assignment evaluate each using the values given

And... one last example where we will look at the fraction bar as a grouping symbol and evaluating the expression when you have more than one of the same variable.

Example 3 - Using the Fraction Bar as a Grouping Symbol

algebra 1 assignment evaluate each using the values given

If you are familiar with the order of operations, then evaluating algebraic expressions is quite easy! Just remember to substitute the given values for each variable and evaluate.

The next lesson in this unit is translating algebraic expressions .

  • Evaluate Expressions

algebra 1 assignment evaluate each using the values given

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1.5.2: Evaluate Single Variable Expressions

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Single Variable Expressions

algebra 1 assignment evaluate each using the values given

Shelly is making bracelets to sell at her town's market this summer. She spent $150 on supplies and will make $4 for every bracelet she sells. Her profit for selling b bracelets is given by the expression 4b−150. How can Shelly calculate her profit if she sells 50 bracelets this summer?

In this concept, you will learn how to evaluate single variable expressions.

Evaluating Single Variable Expressions

An expression is a mathematical phrase that contains numbers and operations.

Here are some examples of expressions:

  • 3+10−5
  • −15+7−1
  • 5 2 −1

A variable is a symbol or letter (such as x,m,R,y,P, or a) that is used to represent a quantity that might change in value. A variable expression is an expression that includes variables. Another name for a variable expression is an algebraic expression .

Here are some examples of variable expressions:

A single variable expression is a variable expression with just one variable in it.

You can use a variable expression to describe a real world situation where one or more quantities has an unknown value or can change in value.

To evaluate a variable expression means to find the value of the expression for a given value of the variable. To evaluate, substitute the given value for the variable in the expression and simplify using the order of operations. To follow the order of operations, you always need to do any multiplication/division first before any addition/subtraction.

Here is an example.

Evaluate the expression 10k−44 for k=12.

First, remember that when you see a number next to a letter, like "10k", it means to multiply.

Next, substitute 12 in for the letter k in the expression.

Notice that you can put parentheses around the 12 to keep it separate from the number 10.

Now, simplify the expression using the order of operations. You will need to multiply first and then subtract.

The answer is 76.

Here is another example that involves division.

Evaluate the expression (x/3)+2 for x=24.

First, remember that a fraction bar is like a division sign. x/3 is the same as x÷3.

Next, substitute 24 in for the letter x in the expression.

Now, simplify the expression using the order of operations. You will need to divide first and then add.

The answer is 10.

Example \(\PageIndex{1}\)

Earlier, you were given a problem about Shelly and her bracelet business.

Shelly is selling bracelets this summer and her profit for selling b bracelets is given by the expression 4b−150. Shelly wants to calculate what her profit will be if she sells 50 bracelets.

To calculate her profit from selling 50 bracelets, Shelly needs to evaluate the expression 4b−150 for b=50.

First, substitute 50 in for the letter b in the expression.

Shelly's profit from selling 50 bracelets would be $50.

Evaluate (x/7)−5 if x is 49.

First, substitute 49 in for the letter x in the expression.

Now, simplify the expression using the order of operations. You will need to divide first and then subtract.

The answer is 2.

Evaluate 4x−9 if x is 20.

First, substitute 20 in for the letter x in the expression.

The answer is 71.

Evaluate 5y+6 if y is 9.

First, substitute 9 in for the letter y in the expression.

Now, simplify the expression using the order of operations. You will need to multiply first and then add.

The answer is 51.

Evaluate (a/4)−8 if a is 36.

First, substitute 36 in for the letter a in the expression.

The answer is 1.

Evaluate each expression if the given value of r is 9.

  • 4r−2r
  • 12r−1

Evaluate each expression for h=12.

  • 70−3h
  • 6h−2h

Review (Answers)

To see the Review answers, open this PDF file and look for section 1.4.

Additional Resources

PLIX: Play, Learn, Interact, eXplore: Single Variable Expressions: Neighborhood Block

Practice: Evaluate Single Variable Expressions

Real World Application: Dog Diets

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Course: Algebra 1   >   Unit 1

  • What is a variable?
  • Why aren't we using the multiplication sign?
  • Creativity break: Why is creativity important in STEM jobs?
  • Evaluating an expression with one variable

Evaluating expressions with one variable

  • Your answer should be
  • an integer, like 6 ‍  
  • a simplified proper fraction, like 3 / 5 ‍  
  • a simplified improper fraction, like 7 / 4 ‍  
  • a mixed number, like 1   3 / 4 ‍  
  • an exact decimal, like 0.75 ‍  
  • a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  

Real Numbers: Algebra Essentials

Evaluating algebraic expressions.

So far, the mathematical expressions we have seen have involved real numbers only. In mathematics, we may see expressions such as [latex]x+5,\frac{4}{3}\pi {r}^{3}[/latex], or [latex]\sqrt{2{m}^{3}{n}^{2}}[/latex]. In the expression [latex]x+5[/latex], 5 is called a constant because it does not vary and x is called a variable because it does. (In naming the variable, ignore any exponents or radicals containing the variable.) An algebraic expression is a collection of constants and variables joined together by the algebraic operations of addition, subtraction, multiplication, and division.

We have already seen some real number examples of exponential notation, a shorthand method of writing products of the same factor. When variables are used, the constants and variables are treated the same way.

In each case, the exponent tells us how many factors of the base to use, whether the base consists of constants or variables.

Any variable in an algebraic expression may take on or be assigned different values. When that happens, the value of the algebraic expression changes. To evaluate an algebraic expression means to determine the value of the expression for a given value of each variable in the expression. Replace each variable in the expression with the given value, then simplify the resulting expression using the order of operations. If the algebraic expression contains more than one variable, replace each variable with its assigned value and simplify the expression as before.

Example 8: Describing Algebraic Expressions

List the constants and variables for each algebraic expression.

  • [latex]\frac{4}{3}\pi {r}^{3}[/latex]
  • [latex]\sqrt{2{m}^{3}{n}^{2}}[/latex]
  • [latex]2\pi r\left(r+h\right)[/latex]
  • [latex]4{y}^{3}+y[/latex]

Example 9: Evaluating an Algebraic Expression at Different Values

Evaluate the expression [latex]2x - 7[/latex] for each value for x.

  • [latex]x=0[/latex]
  • [latex]x=1[/latex]
  • [latex]x=\frac{1}{2}[/latex]
  • [latex]x=-4[/latex]
  • Substitute 0 for [latex]x[/latex]. [latex]\begin{array}\text{ }2x-7 \hfill& = 2\left(0\right)-7 \\ \hfill& =0-7 \\ \hfill& =-7\end{array}[/latex]
  • Substitute 1 for [latex]x[/latex]. [latex]\begin{array}\text{ }2x-7 \hfill& = 2\left(1\right)-7 \\ \hfill& =2-7 \\ \hfill& =-5\end{array}[/latex]
  • Substitute [latex]\frac{1}{2}[/latex] for [latex]x[/latex]. [latex]\begin{array}\text{ }2x-7 \hfill& = 2\left(\frac{1}{2}\right)-7 \\ \hfill& =1-7 \\ \hfill& =-6\end{array}[/latex]
  • Substitute [latex]-4[/latex] for [latex]x[/latex]. [latex]\begin{array}\text{ }2x-7 \hfill& = 2\left(-4\right)-7 \\ \hfill& =-8-7 \\ \hfill& =-15\end{array}[/latex]

Evaluate the expression [latex]11 - 3y[/latex] for each value for y.

a. [latex]y=2[/latex] b. [latex]y=0[/latex] c. [latex]y=\frac{2}{3}[/latex] d. [latex]y=-5[/latex]

Example 10: Evaluating Algebraic Expressions

Evaluate each expression for the given values.

  • [latex]x+5[/latex] for [latex]x=-5[/latex]
  • [latex]\frac{t}{2t - 1}\\[/latex] for [latex]t=10[/latex]
  • [latex]\frac{4}{3}\pi {r}^{3}\\[/latex] for [latex]r=5[/latex]
  • [latex]a+ab+b[/latex] for [latex]a=11,b=-8[/latex]
  • [latex]\sqrt{2{m}^{3}{n}^{2}}[/latex] for [latex]m=2,n=3[/latex]
  • Substitute [latex]-5[/latex] for [latex]x[/latex]. [latex]\begin{array}\text{ }x+5\hfill&=\left(-5\right)+5 \\ \hfill&=0\end{array}[/latex]
  • Substitute 10 for [latex]t[/latex]. [latex]\begin{array}\text{ }\frac{t}{2t-1}\hfill& =\frac{\left(10\right)}{2\left(10\right)-1} \\ \hfill& =\frac{10}{20-1} \\ \hfill& =\frac{10}{19}\end{array}[/latex]
  • Substitute 5 for [latex]r[/latex]. [latex]\begin{array}\text{ }\frac{4}{3}\pi r^{3} \hfill& =\frac{4}{3}\pi\left(5\right)^{3} \\ \hfill& =\frac{4}{3}\pi\left(125\right) \\ \hfill& =\frac{500}{3}\pi\end{array}[/latex]
  • Substitute 11 for [latex]a[/latex] and –8 for [latex]b[/latex]. [latex]\begin{array}\text{ }a+ab+b \hfill& =\left(11\right)+\left(11\right)\left(-8\right)+\left(-8\right) \\ \hfill& =11-8-8 \\ \hfill& =-85\end{array}[/latex]
  • Substitute 2 for [latex]m[/latex] and 3 for [latex]n[/latex]. [latex]\begin{array}\text{ }\sqrt{2m^{3}n^{2}} \hfill& =\sqrt{2\left(2\right)^{3}\left(3\right)^{2}} \\ \hfill& =\sqrt{2\left(8\right)\left(9\right)} \\ \hfill& =\sqrt{144} \\ \hfill& =12\end{array}[/latex]

a. [latex]\frac{y+3}{y - 3}[/latex] for [latex]y=5[/latex] b. [latex]7 - 2t[/latex] for [latex]t=-2[/latex] c. [latex]\frac{1}{3}\pi {r}^{2}[/latex] for [latex]r=11[/latex] d. [latex]{\left({p}^{2}q\right)}^{3}[/latex] for [latex]p=-2,q=3[/latex] e. [latex]4\left(m-n\right)-5\left(n-m\right)[/latex] for [latex]m=\frac{2}{3},n=\frac{1}{3}[/latex]

  • College Algebra. Authored by : OpenStax College Algebra. Provided by : OpenStax. Located at : http://cnx.org/contents/[email protected]:1/Preface . License : CC BY: Attribution

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COMMENTS

  1. PDF Evaluating Variable Expressions

    Kuta Software - Infinite Pre-Algebra Name_____ Evaluating Variable Expressions Date_____ Period____ Evaluate each using the values given. 1) n2 − m; use m = 7, and n = 8 57 2) 8(x − y); use x = 5, and y = 2 24 3) yx ÷ 2; use x = 7, and y = 2 7 4) m − n ÷ 4; use m = 5, and n ...

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    answer answered Algebra 1 Assignment Evaluate each using the values given. 1) 2 - xyl; use x = 7, y = -5, and z = 1 Advertisement godzkoolaid is waiting for your help. Add your answer and earn points. Add answer +5 pts Answer 2 people found it helpful maggiea05 the answer should be -33 i don't know for sure but i think it is arrow right

  4. PDF Unit 1 Corrective Assignment

    Evaluate each expression. 3) ( ) Evaluate each using the values given. 5) y( x ( y y)); use x , and y Write each as an algebraic expression. 7) q increased by 12 is greater than 7 Sovlve using mental math. 9) n

  5. PDF Evaluating Expressions (D)

    Evaluate each expression using the value given. 1. 8b (b=4) 2. 3v (v=3 ) 3. v v (v=8) 4. v v (v=1) 5. 3+v (v=2) 6. 2+c (c=1) 7. v 6 (v=9 8. 5 x (x =5) 9. u2 (u=2) 10. 9 a (a=4) 11. 6+u (u=8) 12. b4 (b=1) 13. b+1 (b=1) 14. 6 c (c=9) 15. u 7 (u=1) Math-Drills.com. Evaluating Expressions (D) Answers Evaluate each expression using the value given ...

  6. Study Guide

    Any variable in an algebraic expression may take on or be assigned different values. When that happens, the value of the algebraic expression changes. To evaluate an algebraic expression means to determine the value of the expression for a given value of each variable in the expression. Replace each variable in the expression with the given ...

  7. Single Variable Expressions ( Read )

    Another name for a variable expression is an algebraic expression. Here are some examples of variable expressions: 3 x + 10. 10 r. b 3 + 2. m x − 3. A single variable expression is a variable expression with just one variable in it. You can use a variable expression to describe a real world situation where one or more quantities has an ...

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    You can pick either one. Let's say you subtract 2x from both sides (this may be a little easier to work with a positive value as a result). - 14 = 2x - 16. 3) To isolate the remaining X term, you need to add 16 to both sides: 2 = 2x. 4) Then, complete the problem by dividing both sides by 2. 1 = x. Hope this helps.

  9. 6.1: Evaluating Algebraic Expressions

    Evaluate the expression ( a − b) 2 If a = 3 and b = −5, at a = 3 and b = −5. Solution. Following "Tips for Evaluating Algebraic Expressions," first replace all occurrences of variables in the expression ( a − b) 2 with open parentheses. (a − b)2 = (() − ())2 ( a − b) 2 = ( () − ()) 2. Secondly, replace each variable with its ...

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  11. Evaluating expressions with one variable

    How to evaluate an expression with one variable Let's say we want to evaluate the expression a + 4 . Well, first we need to know the value of the variable a . For example, to evaluate the expression when a = 1 , we just replace a with 1 : a + 4 = 1 + 4 Replace a with 1. = 5 So, the expression a + 4 equals 5 when a = 1 .

  12. PDF Evaluating Expressions (A)

    Evaluating Expressions (A) Answers 7 b (b = 6) = 1 2. x + 7 (x = 7) = 14 3. 2b (b = 2) = 4 4. y y

  13. 2.3: Evaluate, Simplify, and Translate Expressions (Part 1)

    To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations. Example \ (\PageIndex {1}\): evaluate.

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    Order of Operations and Evaluating Expressions - Word Docs & PowerPoints. 1-2 Assignment - Order of Operations and Evaluating Expressions. 1-2 Bell Work - Order of Operations and Evaluating Expressions. 1-2 Exit Quiz - Order of Operations and Evaluating Expressions. 1-2 Guide Notes SE - Order of Operations and Evaluating Expressions.

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  16. Evaluating and Solving Functions

    When we have a function in formula form, it is usually a simple matter to evaluate the function. For example, the function f (x)= 5−3x2 f ( x) = 5 − 3 x 2 can be evaluated by squaring the input value, multiplying by 3, and then subtracting the product from 5. How To: EVALUATE A FUNCTION Given ITS FORMula.

  17. Evaluate Expressions with One or More Variables

    Multiple Variable Expressions. A common activity in Algebra is to simplify an expression by evaluating it for some given value of the variable. Take a look at this example to see how this works: Let x = 12. Find the value of 2x - 7. To find the solution, substitute 12 in place of x in the given expression. 2x − 7 = 2(12) − 7 = 24 − 7 = 17.

  18. How to Evaluate Algebraic Expressions

    An algebraic expression consists of numbers, variables, and operations. Here are a few examples: In order to evaluate an algebraic expression, you must know the exact values for each variable. Then you will simply substitute and evaluate using the order of operations. Take a look at example 1.

  19. 1.5.2: Evaluate Single Variable Expressions

    Evaluating Single Variable Expressions. An expression is a mathematical phrase that contains numbers and operations.. Here are some examples of expressions: 3+10−5 ; −15+7−1; 5 2 −1; 15(3+4)+2 ; A variable is a symbol or letter (such as x,m,R,y,P, or a) that is used to represent a quantity that might change in value. A variable expression is an expression that includes variables.

  20. Evaluating expressions with one variable

    Evaluating expressions with one variable. Evaluate 9 m + 4 when m = 3 . Stuck? Review related articles/videos or use a hint. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education ...

  21. 5.3 Evaluating Algebraic Expressions

    To evaluate an algebraic expression means to determine the value of the expression for a given value of each variable in the expression. Replace each variable in the expression with the given value then simplify the resulting expression using the order of operations.

  22. Evaluate Expressions with One or More Variables

    evaluate Expression variable (1 more) variable expression. English. Concept Nodes: MAT.ALG.104.03 (Evaluate Expressions with One or More Variables - Algebra) artifactID: 2302606. artifactRevisionID: 25539071. Show. Reviews. Back to the.

  23. Evaluating Algebraic Expressions

    To evaluate an algebraic expression means to determine the value of the expression for a given value of each variable in the expression. Replace each variable in the expression with the given value, then simplify the resulting expression using the order of operations. If the algebraic expression contains more than one variable, replace each ...