2.2 Solve equations using the division and multiplication properties  (Page 3/4)

Solution

Begin by translating the sentence into an equation.

Translate.
Divide by $\mathrm{-11}$ .
Simplify.
Check: $\begin{array}{cccc}& \hfill 143& =& \mathrm{-11}y\hfill \\ & \hfill 143& \stackrel{?}{=}& \mathrm{-11}(\mathrm{-13})\hfill \\ & \hfill 143& =& 143✓\hfill \end{array}$

Solution

Begin by translating the sentence into an equation. Translate.
Multiple both sides by 8.
Simplify.
Check:	Is $n$ divided by 8 equal to −32?
Let $n=\mathrm{-256}$ .	Is $\mathrm{-256}$ divided by $8$ equal to $\mathrm{-32}$ ?
Translate.	$\frac{\mathrm{-256}}{8}\stackrel{?}{=}\mathrm{-32}$
Simplify.	$\mathrm{-32}=\mathrm{-32}✓$

Solution

Begin by translating the sentence into an equation.

Translate.
Multiply both sides by $\mathrm{-4}$ .
Simplify.
Check:	Is the quotient of $y$ and $\mathrm{-4}$ equal to $68$ ?
Let $y=\mathrm{-272}$ .	Is the quotient of $\mathrm{-272}$ and $\mathrm{-4}$ equal to $68$ ?
Translate.	$\frac{\mathrm{-272}}{\mathrm{-4}}\stackrel{?}{=}68$
Simplify.	$68=68✓$

Solution

Begin by translating the sentence into an equation. Remember, “of” translates into multiplication.

Translate.
Multiply both sides by $\frac{4}{3}.$
Simplify.
Check:	Is three-fourths of p equal to 18?
Let $p=24.$	Is three-fourths of 24 equal to 18?
Translate.	$\frac{3}{4}·24\stackrel{?}{=}18$
Simplify.	$18=18✓$

Solution

Begin by translating the sentence into an equation.

Translate.
Subtract $\frac{3}{8}$ from each side.
Simplify and rewrite fractions with common denominators.
Simplify.
Check:		Is the sum of three-eighths and $x$ equal to one-half?
$\text{Let}x=\frac{1}{8}.$		Is the sum of three-eighths and one-eighth equal to one-half?
Translate.		$\frac{3}{8}+\frac{1}{8}\stackrel{?}{=}\frac{1}{2}$
Simplify.		$\frac{4}{8}\stackrel{?}{=}\frac{1}{2}$
Simplify.		$\frac{1}{2}=\frac{1}{2}✓$

Solution

$\begin{array}{cccc}\text{What are you asked to find?}\hfill & & & \text{The cost of 1 pound of grapes}\hfill \\ \\ \\ \text{Assign a variable.}\hfill & & & \text{Let}c=\text{the cost of one pound.}\hfill \\ \\ \\ \begin{array}{c}\text{Write a sentence that gives the}\hfill \\ \text{information to find it.}\hfill \end{array}\hfill & & & \text{The cost of 6 pounds is \$10.74.}\hfill \\ \\ \\ \text{Translate into an equation.}\hfill & & & \begin{array}{ccc}\hfill 6c& =\hfill & 10.74\hfill \end{array}\hfill \\ \text{Solve.}\hfill & & & \begin{array}{ccc}\hfill \frac{6c}{6}& =\hfill & \frac{10.74}{6}\hfill \\ \hfill c& =\hfill & 1.79\hfill \end{array}\hfill \\ \\ \\ & & & \text{The grapes cost \$1.79 per pound.}\hfill \\ \\ \\ \begin{array}{c}\text{Check: If one pound costs \$1.79, do}\hfill \\ \text{6 pounds cost \$10.74?}\hfill \end{array}\hfill & & & \\ \\ \\ \\ \begin{array}{ccc}\hfill 6\left(1.79\right)& \stackrel{?}{=}\hfill & 10.74\hfill \\ \hfill 10.74& =\hfill & 10.74✓\hfill \end{array}\hfill & & & \end{array}$