### 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.

$w\xe2\u02c6\u20198=5,\phantom{\rule{0.2em}{0ex}}w=3$

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

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

$y+2=\mathrm{\xe2\u02c6\u20196}$

$n+3.6=5.1$

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

$x\xe2\u02c6\u20199=\mathrm{\xe2\u02c6\u20194}$

$p\xe2\u02c6\u20194.8=14$

In the following exercises, solve the equation.

$y+16=\mathrm{\xe2\u02c6\u20199}$

$d\xe2\u02c6\u20193.9=8.2$

$7x+10\xe2\u02c6\u20196x+3=5$

$8(3p+5)\xe2\u02c6\u201923(p\xe2\u02c6\u20191)=35$

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.

$13a=\mathrm{\xe2\u02c6\u201965}$

$\xe2\u02c6\u2019y=4$

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

$\frac{y}{\mathrm{\xe2\u02c6\u201910}}=30$

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

In the following exercises, solve each equation.

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

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

$24x+8x\xe2\u02c6\u201911x=\mathrm{\xe2\u02c6\u20197}\mathrm{\xe2\u02c6\u201914}$

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

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

$10w\xe2\u02c6\u20195=65$

$32=\mathrm{\xe2\u02c6\u20194}\xe2\u02c6\u20199n$

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

$5a+21=2a$

$4x\xe2\u02c6\u2019\frac{3}{8}=3x$

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

$5n\xe2\u02c6\u201920=\mathrm{\xe2\u02c6\u20197}n\xe2\u02c6\u201980$

$\frac{5}{8}\phantom{\rule{0.1em}{0ex}}c\xe2\u02c6\u20194=\frac{3}{8}\phantom{\rule{0.1em}{0ex}}c+4$

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

$9(2p\xe2\u02c6\u20195)=72$

$8+3(n\xe2\u02c6\u20199)=17$

$\frac{1}{3}(6m+21)=m\xe2\u02c6\u20197$

$5+7(2\xe2\u02c6\u20195x)=2(9x+1)\xe2\u02c6\u2019(13x\xe2\u02c6\u201957)$

$0.25(q\xe2\u02c6\u20198)=0.1(q+7)$

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

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

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

$\frac{3}{4}\phantom{\rule{0.1em}{0ex}}a\xe2\u02c6\u2019\frac{1}{3}=\frac{1}{2}\phantom{\rule{0.1em}{0ex}}a+\frac{5}{6}$

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

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

$0.36u+2.55=0.41u+6.8$

$0.10d+0.05(d\xe2\u02c6\u20194)=2.05$