Question

which is a solution for the equation below?
$2|1 - 3x| + 5 = 13$
options: $x = \frac{5}{3}$, $x = -4$, $x = 3$, $x = -\frac{10}{3}$

Explanation:

Step1: Isolate the absolute value term

Subtract 5 from both sides:
$2|1-3x| + 5 - 5 = 13 - 5$
$2|1-3x| = 8$

Step2: Simplify the equation

Divide both sides by 2:
$\frac{2|1-3x|}{2} = \frac{8}{2}$
$|1-3x| = 4$

Step3: Split into two cases

Case 1: $1-3x = 4$
Case 2: $1-3x = -4$

Step4: Solve Case 1

Subtract 1, then divide by -3:
$1-3x -1 = 4 -1$
$-3x = 3$
$x = \frac{3}{-3} = -1$

Step5: Solve Case 2

Subtract 1, then divide by -3:
$1-3x -1 = -4 -1$
$-3x = -5$
$x = \frac{-5}{-3} = \frac{5}{3}$

Answer:

A. $x = \frac{5}{3}$