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ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?
Verify a Solution of an Equation
In the following exercises, determine whether each number is a solution to the equation.
$10x-1=5x;x=\frac{1}{5}$
$\mathrm{-12}n+5=8n;n=-\frac{5}{4}$
Solve Equations using the Subtraction and Addition Properties of Equality
In the following exercises, solve each equation using the Subtraction Property of Equality.
$a+\frac{1}{3}=\frac{5}{3}$
In the following exercises, solve each equation using the Addition Property of Equality.
$c-\frac{3}{11}=\frac{9}{11}$
In the following exercises, solve each equation.
$n-12=32$
$f+\frac{2}{3}=4$
Solve Equations That Require Simplification
In the following exercises, solve each equation.
$y+8-15=\mathrm{-3}$
$6(n-1)-5n=\mathrm{-14}$
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 $\mathrm{-6}$ and $m$ is 25.
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?
Tan weighs 146 pounds. Minh weighs 15 pounds more than Tan. How much does Minh weigh?
161 pounds
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?
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
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.
$0.25p=5.25$
$\frac{n}{6}=18$
$36=\frac{3}{4}x$
$\mathrm{-18}m=\mathrm{-72}$
$0.45x=6.75$
Solve Equations That Require Simplification
In the following exercises, solve each equation requiring simplification.
$5r-3r+9r=35-2$
$\frac{11}{12}n-\frac{5}{6}n=9-5$
Translate to an Equation and Solve
In the following exercises, translate to an equation and then solve.
143 is the product of $\mathrm{-11}$ and y .
The quotient of b and and 9 is $\mathrm{-27}$ .
$\frac{b}{9}=\mathrm{-27};b=\mathrm{-243}$
The sum of q and one-fourth is one.
The difference of s and one-twelfth is one fourth.
$s-\frac{1}{12}=\frac{1}{4};s=\frac{1}{3}$
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?
Janet gets paid $24 per hour. She heard that this is $\frac{3}{4}$ of what Adam is paid. How much is Adam paid per hour?
$32
Solve an Equation with Constants on Both Sides
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