Question

solve for x.
|2x - 8| + 12 = 28
if there is more than one solution, separate them with commas. if there is no solution, click on
o solution\.
x =

Explanation:

Step1: Isolate the absolute value

Subtract 12 from both sides of the equation \(|2x - 8| + 12 = 28\) to get \(|2x - 8| = 28 - 12\).
\( |2x - 8| = 16 \)

Step2: Solve the absolute value equation

The absolute value equation \(|A| = B\) (where \(B\geq0\)) has solutions \(A = B\) or \(A = -B\). So we have two cases:

Case 1: \(2x - 8 = 16\)

Add 8 to both sides: \(2x = 16 + 8\)
\(2x = 24\)
Divide both sides by 2: \(x = \frac{24}{2}\)
\(x = 12\)

Case 2: \(2x - 8 = -16\)

Add 8 to both sides: \(2x = -16 + 8\)
\(2x = -8\)
Divide both sides by 2: \(x = \frac{-8}{2}\)
\(x = -4\)

Answer:

12, -4