Questions: What is the solution set of the equation below? x + 4 = 3x - 12 A. ∅ B. 5 E. 8 . 5,8

Solution Steps

The equation is \( |x + 4| = 3x - 12 \). An absolute value equation \( |A| = B \) has two cases:

1. \( A = B \)
2. \( A = -B \)

Set \( x + 4 = 3x - 12 \) and solve for \( x \): \[ x + 4 = 3x - 12 \] Subtract \( x \) from both sides: \[ 4 = 2x - 12 \] Add \( 12 \) to both sides: \[ 16 = 2x \] Divide by \( 2 \): \[ x = 8 \]

Set \( x + 4 = -3x + 12 \) and solve for \( x \): \[ x + 4 = -3x + 12 \] Add \( 3x \) to both sides: \[ 4x + 4 = 12 \] Subtract \( 4 \) from both sides: \[ 4x = 8 \] Divide by \( 4 \): \[ x = 2 \]

For \( x = 8 \): \[ |8 + 4| = 3(8) - 12 \implies 12 = 12 \quad \text{(Valid)} \]

For \( x = 2 \): \[ |2 + 4| = 3(2) - 12 \implies 6 = -6 \quad \text{(Invalid)} \]

Only \( x = 8 \) is valid.

Final Answer