CPM Homework Help : INT2 Problem 5-92

One way to solve absolute value equations is to think about “looking inside” the absolute value. The expression inside the absolute value symbol can be positive or negative, so you should solve the equation both ways. For example, you can record your steps as shown at right. Solve each equation. Be sure to determine all possible answers and check your solutions.

$\left|5-2x\right|=19$
$\swarrow$ $\searrow$

$\begin{align}5-2x&=19\\ -2x&=14\\x&=-7\end{align}$ or $\begin{align}5-2x&=-19\\-2x&=-24\\x&=12\end{align}$

$\left| 9 + 3x \right|= 39$
Answer (a):
$x = 10$ or $x = −16$
Step (a):
Create two equations, then solve each for $x$ .
$9 + 3x = 39$
$9 + 3x = −39$

$\left| 2 x + 1 \right|= 10$
Hint (b):
See the help for part (a).
Answer (b):
$x=\frac{9}{2},\text{ or }x= -\frac{11}{2}$

$\left |-3 x + 9 \right |= 10$
Hint (c):
See the help for part (a).

$\left| 3.2 x - 4 \right|= −5.7$
Answer (d):
No solution. Explain why.