Question

solve the absolute value equation.
$left|\frac{x}{3} - 4\
ight| = 2$

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is {}.
(type an integer or a simplified fraction. use a comma to separate answers as needed )
b. the solution set is $\varnothing$.

Explanation:

Step1: Split absolute value equation

$\frac{x}{3}-4=2$ or $\frac{x}{3}-4=-2$

Step2: Solve first equation

Add 4 to both sides: $\frac{x}{3}=2+4=6$
Multiply by 3: $x=6\times3=18$

Step3: Solve second equation

Add 4 to both sides: $\frac{x}{3}=-2+4=2$
Multiply by 3: $x=2\times3=6$

Answer:

A. The solution set is {6, 18}