### Review Exercises

##### Solve Equations using the Subtraction and Addition Properties of Equality

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

$w-8=5,\phantom{\rule{0.2em}{0ex}}w=3$

$4a=72,\phantom{\rule{0.2em}{0ex}}a=18$

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

$y+2=\mathrm{-6}$

$n+3.6=5.1$

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

$x-9=\mathrm{-4}$

$p-4.8=14$

In the following exercises, solve the equation.

$y+16=\mathrm{-9}$

$d-3.9=8.2$

$7x+10-6x+3=5$

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

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

Four less than $n$ is $13.$

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

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

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

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

##### Solve Equations using the Division and Multiplication Properties of Equality

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

$13a=\mathrm{-65}$

$-y=4$

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

$\frac{y}{\mathrm{-10}}=30$

$\frac{5}{8}\phantom{\rule{0.1em}{0ex}}u=\frac{15}{16}$

In the following exercises, solve each equation.

$\frac{c}{9}=36$

$\frac{11}{12}=\frac{2}{3}\phantom{\rule{0.1em}{0ex}}y$

$24x+8x-11x=\mathrm{-7}\mathrm{-14}$

##### Solve Equations with Variables and Constants on Both Sides

In the following exercises, solve the equations with constants on both sides.

$10w-5=65$

$32=\mathrm{-4}-9n$

In the following exercises, solve the equations with variables on both sides.

$5a+21=2a$

$4x-\frac{3}{8}=3x$

In the following exercises, solve the equations with constants and variables on both sides.

$5n-20=\mathrm{-7}n-80$

$\frac{5}{8}\phantom{\rule{0.1em}{0ex}}c-4=\frac{3}{8}\phantom{\rule{0.1em}{0ex}}c+4$

In the following exercises, solve each linear equation using the general strategy.

$9(2p-5)=72$

$8+3(n-9)=17$

$\frac{1}{3}(6m+21)=m-7$

$5+7(2-5x)=2(9x+1)-(13x-57)$

$0.25(q-8)=0.1(q+7)$

##### Solve Equations with Fraction or Decimal Coefficients

In the following exercises, solve each equation by clearing the fractions.

$\frac{1}{3}\phantom{\rule{0.1em}{0ex}}x+\frac{1}{5}\phantom{\rule{0.1em}{0ex}}x=8$

$\frac{3}{4}\phantom{\rule{0.1em}{0ex}}a-\frac{1}{3}=\frac{1}{2}\phantom{\rule{0.1em}{0ex}}a+\frac{5}{6}$

$\frac{1}{2}(k+3)=\frac{1}{3}(k+16)$

In the following exercises, solve each equation by clearing the decimals.

$0.36u+2.55=0.41u+6.8$

$0.10d+0.05(d-4)=2.05$