# 2.2E: Exercises

- Page ID
- 30106

## Practice Makes Perfect

**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.

\(8x=56\)

**Answer**-
\(x=7\)

\(7 p=63\)

\(-5 c=55\)

**Answer**-
\(c=-11\)

\(-9 x=-27\)

\(-809=15 y\)

**Answer**-
\(y = -\frac{809}{15}\)

\(-731=19 y\)

\(-37 p=-541\)

**Answer**-
\(p=-\frac{541}{37}\)

\(-19 m=-586\)

\(0.25 z=3.25\)

**Answer**-
z= 13

\(0.75 a=11.25\)

\(-13x=0\)

**Answer**-
\(x=0\)

\(24x=0\)

\(\frac{x}{4} = 35\)

**Answer**-
\(x=140\)

\(\frac{z}{2}=54\)

\(-20=\frac{q}{-5}\)

**Answer**-
\(q=100\)

\(\frac{c}{-3}=-12\)

\(\frac{y}{9}=-16\)

**Answer**-
\(y=-144\)

\(\frac{q}{6}=-38\)

\(\frac{m}{-12}=45\)

**Answer**-
\(m=-540\)

\(-24=\frac{p}{-20}\)

\(-y=6\)

**Answer**-
\(y=-6\)

\(-u=15\)

\(-v=-72\)

**Answer**-
\(v=72\)

\(-x=-39\)

\(\frac{2}{3} y=48\)

**Answer**-
\(y=72\)

\(\frac{3}{5} r=75\)

\(-\frac{5}{8} w=40\)

**Answer**-
\(w=-64\)

\(24=-\frac{3}{4} x\)

\(-\frac{2}{5}=\frac{1}{10} a\)

**Answer**-
\(a=-4\)

\(-\frac{1}{3} q=-\frac{5}{6}\)

\(-\frac{7}{10} x=-\frac{14}{3}\)

**Answer**-
\(x=\frac{20}{3}\)

\(\frac{3}{8} y=-\frac{1}{4}\)

\(\frac{7}{12}=-\frac{3}{4} p\)

**Answer**-
\(p=-\frac{7}{9}\)

\(\frac{11}{18}=-\frac{5}{6} q\)

\(-\frac{5}{18}=-\frac{10}{9} u\)

**Answer**-
\(u=\frac{1}{4}\)

\(-\frac{7}{20}=-\frac{7}{4} v\)

**Solve Equations That Require Simplification**

In the following exercises, solve each equation requiring simplification.

\(100-16=4 p-10 p-p\)

**Answer**-
\(p=-12\)

\(-18-7=5 t-9 t-6 t\)

\(\frac{7}{8} n-\frac{3}{4} n=9+2\)

**Answer**-
\(n=88\)

\(\frac{5}{12} q+\frac{1}{2} q=25-3\)

\(0.25 d+0.10 d=6-0.75\)

**Answer**-
d=15

\(0.05 p-0.01 p=2+0.24\)

\(-10(q-4)-57=93\)

**Answer**-
\(q=-11\)

\(-12(d-5)-29=43\)

\(-10(x+4)-19=85\)

**Answer**-
\(x=-\frac{72}{5}\)

\(-15(z+9)-11=75\)

**Mixed Practice**

In the following exercises, solve each equation.

\(\frac{9}{10} x=90\)

**Answer**-
\(x=100\)

\(\frac{5}{12} y=60\)

\(y+46=55\)

**Answer**-
\(y=9\)

\(x+33=41\)

\(\frac{w}{-2}=99\)

**Answer**-
\(w=-198\)

\(\frac{s}{-3}=-60\)

\(27=6 a\)

**Answer**-
\(a=\frac{9}{2}\)

\(-a=7\)

\(-x=2\)

**Answer**-
\(x=-2\)

\(z-16=-59\)

\(m-41=-14\)

**Answer**-
\(m=27\)

\(0.04 r=52.60\)

\(63.90=0.03 p\)

**Answer**-
\(p=2130\)

\(-15 x=-120\)

\(84=-12 z\)

**Answer**-
\(y=-7\)

\(19.36=x-0.2 x\)

\(c-0.3 c=35.70\)

**Answer**-
\(c=51\)

\(-y=-9\)

\(-x=-8\)

**Answer**-
\(x=8\)

**Translate to an Equation and Solve**

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

187 is the product of \(-17\) and \(m\)

133 is the product of \(-19\) and \(n\)

**Answer**-
\(133=-19 n ; n=-7\)

\(-184\) is the product of 23 and \(p\)

\(-152\) is the product of 8 and \(q\)

**Answer**-
\(-152=8 q ; q=-19\)

\(u\) divided by 7 is equal to \(-49\)

\(r\) divided by 12 is equal to \(-48\)

**Answer**-
\(\frac{r}{12}=-48 ; r=-576\)

\(h\) divided by \(-13\) is equal to \(-65\)

\(j\) divided by \(-20\) is equal to \(-80\)

**Answer**-
\(\frac{j}{-20}=-80 ; j=1,600\)

The quotient \(c\) and \(-19\) is \(38 .\)

The quotient of \(b\) and \(-6\) is 18

**Answer**-
\(\frac{b}{-6}=18 ; b=-108\)

The quotient of \(h\) and 26 is \(-52\)

The quotient \(k\) and 22 is \(-66\)

**Answer**-
\(\frac{k}{22}=-66 ; k=-1,452\)

Five-sixths of \(y\) is 15

Three-tenths of \(x\) is 15

**Answer**-
\(\frac{3}{10} x=15 ; x=50\)

Four-thirds of \(w\) is 36

Five-halves of \(v\) is 50

**Answer**-
\(\frac{5}{2} v=50 ; v=20\)

The sum of nine-tenths and \(g\) is two-thirds.

The sum of two-fifths and \(f\) is one-half.

**Answer**-
\(\frac{2}{5}+f=\frac{1}{2} ; f=\frac{1}{10}\)

The difference of \(p\) and one-sixth is two-thirds.

The difference of \(q\) and one-eighth is three-fourths.

**Answer**-
\(q-\frac{1}{8}=\frac{3}{4} ; q=\frac{7}{8}\)

**Translate and Solve Applications**

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

**Kindergarten** Connie’s kindergarten class has 24 children. She wants them to get into 4 equal groups. How many children will she put in each group?

**Balloons** Ramona bought 18 balloons for a party. She wants to make 3 equal bunches. How many balloons did she use in each bunch?

**Answer**-
6 balloons

**Tickets** Mollie paid $36.25 for 5 movie tickets. What was the price of each ticket?

**Shopping** Serena paid $12.96 for a pack of 12 pairs of sport socks. What was the price of pair of sport socks?

**Answer**-
$1.08

**Sewing** Nancy used 14 yards of fabric to make flags for one-third of the drill team. How much fabric, would Nancy need to make flags for the whole team?

**MPG** John’s SUV gets 18 miles per gallon (mpg). This is half as many mpg as his wife’s hybrid car. How many miles per gallon does the hybrid car get?

**Answer**-
36 mpg

**Height** Aiden is 27 inches tall. He is \(\frac{3}{8}\) as tall as his father. How tall is his father?

**Real estate** Bea earned \(\$ 11,700\) commission for selling a house, calculated as \(\frac{6}{100}\) of the selling price. What was the selling

price of the house?

**Answer**-
$195,000

## Everyday Math

**Commissions** Every week Perry gets paid \(\$150\) plus 12% of his total sales amount. Solve the equation

\(840=150+0.12(a-1250)\) for \(a\) to find the total amount Perry must sell in order to be paid \(\$ 840\) one week.

**Stamps** Travis bought $9.45 worth of 49-cent stamps and 21-cent stamps. The number of 21-cent stamps was 5 less than the number of 49-cent stamps. Solve the equation 0.49s+0.21(s−5)=9.45 for *s*, to find the number of 49-cent stamps Travis bought.

**Answer**-
15 49-cent stamps

## Writing Exercises

Frida started to solve the equation −3x=36 by adding 3 to both sides. Explain why Frida’s method will not solve the equation.

Emiliano thinks \(x=40\) is the solution to the equation \(\frac{1}{2} x=80 .\) Explain why he is wrong.

**Answer**-
Answers will vary.

## Self Check

ⓐ 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?