Question

solve for x.
|4x - 12| = 16
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.

Explanation:

Step1: Apply absolute value definition

If \(|a| = b\) (\(b\geq0\)), then \(a = b\) or \(a=-b\). So for \(|4x - 12|=16\), we have two cases:
Case 1: \(4x - 12 = 16\)
Case 2: \(4x - 12=-16\)

Step2: Solve Case 1: \(4x - 12 = 16\)

Add 12 to both sides: \(4x=16 + 12\)
\(4x=28\)
Divide both sides by 4: \(x=\frac{28}{4}=7\)

Step3: Solve Case 2: \(4x - 12=-16\)

Add 12 to both sides: \(4x=-16 + 12\)
\(4x=-4\)
Divide both sides by 4: \(x=\frac{-4}{4}=-1\)

Answer:

\(7, - 1\)