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