5. \( \frac{1}{2}(x-4)=-8 \)

To solve the equation \( \frac{1}{2}(x-4)=-8 \), start by eliminating the fraction. Multiply both sides by 2, giving \( x - 4 = -16 \). Now, add 4 to both sides to isolate \( x \): \( x = -16 + 4 \). This simplifies to \( x = -12 \). So, there you have it – \( x = -12 \)! Now, let’s check our work: Substitute \( -12 \) back into the original equation. \( \frac{1}{2}(-12-4) = \frac{1}{2}(-16) = -8 \). The left side equals the right side, confirming our solution is correct!