three sides of the inequality. \( x+5<12 \) (2) \( |x+5|=12 \) Set it up as \( x+5=12 \) or \( x+5=-12 \) and then solve for \( x \) by subtracting 5 from both sides of each equation. (3) \( |x+5|>12 \)

Let's solve each part of the problem step by step. ### Part 1: Solve the inequality \( x + 5 < 12 \) 1. Start with the inequality: \[ x + 5 < 12 \] 2. Subtract 5 from both sides: \[ x < 12 - 5 \] 3. Simplify: \[ x < 7 \] ### Part 2: Solve the equation \( |x + 5| = 12 \) 1. Set up the two equations based on the absolute value: \[ x + 5 = 12 \quad \text{or} \quad x + 5 = -12 \] 2. Solve the first equation: - Subtract 5 from both sides: \[ x = 12 - 5 \] - Simplify: \[ x = 7 \] 3. Solve the second equation: - Subtract 5 from both sides: \[ x = -12 - 5 \] - Simplify: \[ x = -17 \] So, the solutions for \( |x + 5| = 12 \) are: \[ x = 7 \quad \text{and} \quad x = -17 \] ### Part 3: Solve the inequality \( |x + 5| > 12 \) 1. Set up the two inequalities based on the absolute value: \[ x + 5 > 12 \quad \text{or} \quad x + 5 < -12 \] 2. Solve the first inequality: - Subtract 5 from both sides: \[ x > 12 - 5 \] - Simplify: \[ x > 7 \] 3. Solve the second inequality: - Subtract 5 from both sides: \[ x < -12 - 5 \] - Simplify: \[ x < -17 \] So, the solutions for \( |x + 5| > 12 \) are: \[ x > 7 \quad \text{or} \quad x < -17 \] ### Summary of Solutions 1. For \( x + 5 < 12 \): \( x < 7 \) 2. For \( |x + 5| = 12 \): \( x = 7 \) or \( x = -17 \) 3. For \( |x + 5| > 12 \): \( x > 7 \) or \( x < -17 \)