Question

solve for all values of x in simplest form. -|x + 4| + 8 = 4

Explanation:

Step1: Isolate the absolute value term

Subtract 8 from both sides of the equation \(-|x + 4| + 8 = 4\).
\(-|x + 4| = 4 - 8\)
\(-|x + 4| = -4\)
Multiply both sides by -1 to get \(|x + 4| = 4\).

Step2: Solve the absolute value equation

The absolute value equation \(|x + 4| = 4\) means that \(x + 4 = 4\) or \(x + 4 = -4\).

For \(x + 4 = 4\):

Subtract 4 from both sides: \(x = 4 - 4\)
\(x = 0\)

For \(x + 4 = -4\):

Subtract 4 from both sides: \(x = -4 - 4\)
\(x = -8\)

Answer:

\(x = 0\) or \(x = -8\)