Question

solve the following absolute value equation
-2|x - 4| + 7 = -3
x =

Explanation:

Step1: Isolate the absolute value term

Subtract 7 from both sides of the equation \(-2|x - 4|+7=-3\).
We get \(-2|x - 4|=-3 - 7\), which simplifies to \(-2|x - 4|=-10\).

Step2: Solve for the absolute value

Divide both sides by -2: \(|x - 4|=\frac{-10}{-2}=5\).

Step3: Solve the two cases for absolute value

Case 1: \(x - 4 = 5\)
Add 4 to both sides: \(x=5 + 4=9\).
Case 2: \(x - 4=-5\)
Add 4 to both sides: \(x=-5 + 4=-1\).

Answer:

\(x = 9\) or \(x=-1\)