Question

solve |8 - 4x| = 16. options: x=2, x=24; x=-2, x=6; x=-2, x=-6; no solution

Explanation:

Step1: Recall absolute value definition

For \(|A| = B\) (\(B\geq0\)), \(A = B\) or \(A=-B\). So for \(|8 - 4x| = 16\), we have two cases:
Case 1: \(8 - 4x = 16\)
Case 2: \(8 - 4x = -16\)

Step2: Solve Case 1 (\(8 - 4x = 16\))

Subtract 8 from both sides: \(-4x = 16 - 8 = 8\)
Divide by -4: \(x=\frac{8}{-4}=-2\)

Step3: Solve Case 2 (\(8 - 4x = -16\))

Subtract 8 from both sides: \(-4x=-16 - 8=-24\)
Divide by -4: \(x=\frac{-24}{-4}=6\)

Answer:

\(x = -2, x = 6\) (corresponding to the second option: \(x=-2, x=6\))