Question

solve the absolute value equation: (left|\frac{x}{4}-5
ight| = 1) select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the solution set is (\boxed{quad}) (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

$\frac{x}{4}-5 = 1$ or $\frac{x}{4}-5 = -1$

Step2: Solve first equation

Add 5 to both sides:
$\frac{x}{4}=1+5=6$
Multiply by 4:
$x=6\times4=24$

Step3: Solve second equation

Add 5 to both sides:
$\frac{x}{4}=-1+5=4$
Multiply by 4:
$x=4\times4=16$

Answer:

A. The solution set is {16, 24}