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

Since $|a|=b$ ($b\geq0$) is equivalent to $a = b$ or $a=-b$, we set up two equations:

• Equation 1: $-2x + 6=6$. Subtract 6 from both sides: $-2x+6 - 6=6 - 6$, so $-2x=0$. Then divide both sides by $-2$: $x = 0$.
• Equation 2: $-2x + 6=-6$. Subtract 6 from both sides: $-2x+6 - 6=-6 - 6$, so $-2x=-12$. Then divide both sides by $-2$: $x = 6$.

Answer:

$x = 0$ or $x = 6$