Question

what is the solution to -4|-2x + 6| = -24?
x = 0
x = 0 or x = -6
x = 0 or x = 6
no solution

Explanation:

Step1: Isolate the absolute - value expression

Divide both sides of the equation \(-4|-2x + 6|=-24\) by \(-4\).
\(\frac{-4|-2x + 6|}{-4}=\frac{-24}{-4}\), which simplifies to \(|-2x + 6| = 6\).

Step2: Set up two cases

Case 1: When \(-2x+6\) is non - negative (\(-2x + 6\geq0\)), the equation becomes \(-2x + 6=6\).
Subtract 6 from both sides: \(-2x+6 - 6=6 - 6\), so \(-2x=0\). Then divide by \(-2\): \(x = 0\).
Case 2: When \(-2x + 6\) is negative (\(-2x+6\lt0\)), the equation becomes \(-(-2x + 6)=6\).
Expand the left - hand side: \(2x-6 = 6\). Add 6 to both sides: \(2x-6 + 6=6 + 6\), so \(2x=12\). Divide by 2: \(x = 6\).

Answer:

C. \(x = 0\) or \(x = 6\)