Page 5 of 5 Question 5 Set it up as \( x+5>12 \) or \( x+5<-12 \) and then solve for \( x \) by subtracting 5 from both sides of each inequality. Mrompts each equation or inequality with the correct descri solve for \( x \) by subtracting 5 from both sides of the inequality: (1) \( x+5<12 \) Set it up as \( -12

Ask by Gibbs Franklin. in the United States

Jan 24,2025

Let's solve each part of the problem step by step. ### (1) Solve the inequality \( x + 5 < 12 \) 1. **Set up the inequality**: \[ x + 5 < 12 \] 2. **Subtract 5 from both sides**: \[ x < 12 - 5 \] \[ x < 7 \] ### (2) Set up the compound inequality \( -12 < x + 5 < 12 \) 1. **Set up the compound inequality**: \[ -12 < x + 5 < 12 \] 2. **Subtract 5 from all three sides**: \[ -12 - 5 < x + 5 - 5 < 12 - 5 \] \[ -17 < x < 7 \] ### (3) Solve the equation \( |x + 5| = 12 \) 1. **Set up the two equations**: \[ x + 5 = 12 \quad \text{or} \quad x + 5 = -12 \] 2. **Solve each equation by subtracting 5**: - For \( x + 5 = 12 \): \[ x = 12 - 5 \] \[ x = 7 \] - For \( x + 5 = -12 \): \[ x = -12 - 5 \] \[ x = -17 \] ### (4) Solve the inequality \( |x + 5| < 12 \) 1. **Set up the compound inequality**: \[ -12 < x + 5 < 12 \] 2. **Subtract 5 from all three sides**: \[ -12 - 5 < x + 5 - 5 < 12 - 5 \] \[ -17 < x < 7 \] ### Summary of Results 1. For \( x + 5 < 12 \): \( x < 7 \) 2. For \( -12 < x + 5 < 12 \): \( -17 < x < 7 \) 3. For \( |x + 5| = 12 \): \( x = 7 \) or \( x = -17 \) 4. For \( |x + 5| < 12 \): \( -17 < x < 7 \) These results provide the solutions for each part of the problem.