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Solve: $8x+9x5x=\mathrm{3}+15.$
Start by combining like terms to simplify each side.
Combine like terms.  
Divide both sides by 12 to isolate x.  
Simplify.  
Check your answer. Let $x=1$  
Solve: $1120=17y8y6y.$
Simplify each side by combining like terms.
Simplify each side.  
Divide both sides by 3 to isolate y.  
Simplify.  
Check your answer. Let $y=\mathrm{3}$  
Notice that the variable ended up on the right side of the equal sign when we solved the equation. You may prefer to take one more step to write the solution with the variable on the left side of the equal sign.
Solve: $\mathrm{3}(n2)6=21.$
Remember—always simplify each side first.
Distribute.  
Simplify.  
Divide both sides by 3 to isolate n. 

Check your answer. Let $n=\mathrm{7}$ .  
Solve Equations Using the Division and Multiplication Properties of Equality
In the following exercises, solve each equation for the variable using the Division Property of Equality and check the solution.
$\mathrm{5}c=55$
$\mathrm{90}=6y$
$\mathrm{16}p=\mathrm{64}$
$0.25z=3.25$
$\mathrm{3}x=0$
In the following exercises, solve each equation for the variable using the Multiplication Property of Equality and check the solution.
$\frac{x}{4}=15$
$\mathrm{20}=\frac{\phantom{\rule{0.4em}{0ex}}q}{\mathrm{5}}$
$\frac{\phantom{\rule{0.4em}{0ex}}c}{\mathrm{3}}=\mathrm{12}$
36
$\frac{y}{9}=\mathrm{6}$
$\frac{m}{\mathrm{12}}=5$
$\frac{2}{3}\phantom{\rule{0.1em}{0ex}}y=18$
$\frac{5}{8}\phantom{\rule{0.1em}{0ex}}w=40$
$\frac{2}{5}=\frac{1}{10}\phantom{\rule{0.1em}{0ex}}a$
Solve Equations That Need to be Simplified
In the following exercises, solve the equation.
$8a+3a6a=\mathrm{17}+27$
$\mathrm{9}x9x+2x=502$
$10016=4p10pp$
$\frac{7}{8}\phantom{\rule{0.1em}{0ex}}n\frac{3}{4}\phantom{\rule{0.1em}{0ex}}n=9+2$
$\frac{5}{12}\phantom{\rule{0.1em}{0ex}}q+\frac{1}{2}\phantom{\rule{0.1em}{0ex}}q=253$
q = 24
$0.25d+0.10d=60.75$
Balloons Ramona bought $18$ balloons for a party. She wants to make $3$ equal bunches. Find the number of balloons in each bunch, $b,$ by solving the equation $3b=18.$
Teaching Connie’s kindergarten class has $24$ children. She wants them to get into $4$ equal groups. Find the number of children in each group, $g,$ by solving the equation $4g=24.$
6 children
Ticket price Daria paid $\text{\$36.25}$ for $5$ children’s tickets at the ice skating rink. Find the price of each ticket, $p,$ by solving the equation $5p=36.25.$
Unit price Nishant paid $\text{\$12.96}$ for a pack of $12$ juice bottles. Find the price of each bottle, $b,$ by solving the equation $12b=12.96.$
$1.08
Fuel economy Tania’s SUV gets half as many miles per gallon (mpg) as her husband’s hybrid car. The SUV gets $\text{18 mpg}.$ Find the miles per gallons, $m,$ of the hybrid car, by solving the equation $\frac{1}{2}\phantom{\rule{0.1em}{0ex}}m=18.$
Fabric The drill team used $14$ yards of fabric to make flags for onethird of the members. Find how much fabric, $f,$ they would need to make flags for the whole team by solving the equation $\frac{1}{3}\phantom{\rule{0.1em}{0ex}}f=14.$
42 yards
Frida started to solve the equation $\mathrm{3}x=36$ by adding $3$ to both sides. Explain why Frida’s method will result in the correct solution.
Emiliano thinks $x=40$ is the solution to the equation $\frac{1}{2}\phantom{\rule{0.1em}{0ex}}x=80.$ Explain why he is wrong.
Answer will vary.
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ After reviewing this checklist, what will you do to become confident for all objectives?
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