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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This is a table that has six rows and four columns. In the first row, which is a header row, the cells read from left to right: “I can…,” “confidently,” “with some help,” and “no-I don’t get it!” The first column below “I can…” reads “graph inequalities on the number line,” “solve inequalitites using the Subtraction and Addition Properties of Inequality,” “solve inequalitites using the Division and Multiplication Properties of Inequality,” “solve inequalities that require simplification,” and “translate to an inequality and solve.” The rest of the cells are blank.

What does this checklist tell you about your mastery of this section? What steps will you take to improve?

Chapter 2 review exercises

Section 2.1 Solve Equations using the Subtraction and Addition Properties of Equality

Verify a Solution of an Equation

In the following exercises, determine whether each number is a solution to the equation.

10 x 1 = 5 x ; x = 1 5

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w + 2 = 5 8 ; w = 3 8

no

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−12 n + 5 = 8 n ; n = 5 4

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6 a 3 = −7 a , a = 3 13

yes

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Solve Equations using the Subtraction and Addition Properties of Equality

In the following exercises, solve each equation using the Subtraction Property of Equality.

In the following exercises, solve each equation using the Addition Property of Equality.

In the following exercises, solve each equation.

d 3.9 = 8.2

d = 12.1

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Solve Equations That Require Simplification

In the following exercises, solve each equation.

7 x + 10 6 x + 3 = 5

x = −8

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6 ( n 1 ) 5 n = −14

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8 ( 3 p + 5 ) 23 ( p 1 ) = 35

p = −28

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Translate to an Equation and Solve

In the following exercises, translate each English sentence into an algebraic equation and then solve it.

The sum of −6 and m is 25.

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Four less than n is 13.

n 4 = 13 ; n = 17

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Translate and Solve Applications

In the following exercises, translate into an algebraic equation and solve.

Rochelle’s daughter is 11 years old. Her son is 3 years younger. How old is her son?

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Tan weighs 146 pounds. Minh weighs 15 pounds more than Tan. How much does Minh weigh?

161 pounds

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Peter paid $9.75 to go to the movies, which was $46.25 less than he paid to go to a concert. How much did he pay for the concert?

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Elissa earned $152.84 this week, which was $21.65 more than she earned last week. How much did she earn last week?

$131.19

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Section 2.2 Solve Equations using the Division and Multiplication Properties of Equality

Solve Equations Using the Division and Multiplication Properties of Equality

In the following exercises, solve each equation using the division and multiplication properties of equality and check the solution.

Solve Equations That Require Simplification

In the following exercises, solve each equation requiring simplification.

5 r 3 r + 9 r = 35 2

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24 x + 8 x 11 x = −7 14

x = −1

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11 12 n 5 6 n = 9 5

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−9 ( d 2 ) 15 = −24

d = 3

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Translate to an Equation and Solve

In the following exercises, translate to an equation and then solve.

143 is the product of −11 and y .

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The quotient of b and and 9 is −27 .

b 9 = −27 ; b = −243

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The sum of q and one-fourth is one.

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The difference of s and one-twelfth is one fourth.

s 1 12 = 1 4 ; s = 1 3

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Translate and Solve Applications

In the following exercises, translate into an equation and solve.

Ray paid $21 for 12 tickets at the county fair. What was the price of each ticket?

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Janet gets paid $24 per hour. She heard that this is 3 4 of what Adam is paid. How much is Adam paid per hour?

$32

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Section 2.3 Solve Equations with Variables and Constants on Both Sides

Solve an Equation with Constants on Both Sides

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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