1. **Stating the problem:** Solve the equation $|3x + 4| = |2x + 6|$. 2. **Formula and rules:** The absolute value equation $|A| = |B|$ implies either $A = B$ or $A = -B$. 3. **Set up the two cases:** Case 1: $3x + 4 = 2x + 6$ Case 2: $3x + 4 = -(2x + 6)$ 4. **Solve Case 1:** $3x + 4 = 2x + 6$ Subtract $2x$ from both sides: $3x - 2x + 4 = 6$ Simplify: $x + 4 = 6$ Subtract 4: $x = 2$ 5. **Solve Case 2:** $3x + 4 = -2x - 6$ Add $2x$ to both sides: $3x + 2x + 4 = -6$ Simplify: $5x + 4 = -6$ Subtract 4: $5x = -10$ Divide by 5: $x = -2$ 6. **Final answer:** The solutions are $x = 2$ and $x = -2$. These values satisfy the original equation because the absolute values make both sides positive or equal in magnitude.