Question

solve.
|2x - (3x - 5)| = 7
a. {-4, 4}
b. {-\frac{2}{3}, 4}
c. {-4, \frac{2}{3}}
d. {-\frac{2}{3}, \frac{2}{3}}

Explanation:

Step1: Remove absolute value

$2x - (5x - 5) = 7$ or $2x - (5x - 5) = -7$

Step2: Simplify first equation

$-3x + 5 = 7$
$-3x = 2$
$x = -\frac{2}{3}$

Step3: Simplify second equation

$-3x + 5 = -7$
$-3x = -12$
$x = 4$

Step4: Combine solutions

The solution set is $\{-\frac{2}{3}, 4\}$

Answer:

B. $\{-\frac{2}{3}, 4\}$