CPM Homework Help : CC2 Problem 8-40

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8-40.

Simplify and solve each equation below for $x$ . Show your work and check your answer.

$24 = 3 x + 3$
Step 1 (a):
Begin isolating $x$ by subtracting $3$ from both sides.
$\begin{array}{l} \; 24=3x+3\\ -3 \qquad \; \, -3\\ \; 21=3x \end{array}$
Step 2 (a):
Divide both sides by $3$ .
$\frac{21}{3}=\frac{3\textit{x}}{3}$
Answer (a):
$x=7$

$2(x-6)=x-14$
Hint (b):
Begin by distributing.
More (b):
$\begin{array}{r} 2(x)-2(6)=x-14\\ 2x-12=x-14 \end{array}$
Add $12$ to both sides.
Next (b):
$2x=x-2$
Subtract $x$ from each side.
Answer (b):
$x=-2$

$3(2x-3)=4x-5$
Hint (c):
Follow the methods presented in parts (a) and (b).

$\frac{3}{4}x=2x-5$
Hint (d):
Follow the methods presented in parts (a) and (b).

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