Page 5 of 5 Question 5 Set it up as $$ x+512 $$ or $$ x+5

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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

UpStudy AI · Accepted Answer

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.
Solutions: 1. $$ x < 7 $$ 2. $$ -17 < x < 7 $$ 3. $$ x = 7 $$ or $$ x = -17 $$ 4. $$ -17 < x < 7 $$

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