We will solve the inequality \( -24 \leq -3x - 3 \) or \( -39 > -3x - 3 \).

### First Inequality:
\[ -24 \leq -3x - 3 \]
1. Add 3 to both sides:
   \[
   -24 + 3 \leq -3x
   \]
   \[
   -21 \leq -3x
   \]
2. Divide by \(-3\) (remember to reverse the inequality when dividing by a negative number):
   \[
   \frac{-21}{-3} \geq x
   \]
   \[
   7 \geq x \quad \text{or} \quad x \leq 7
   \]

### Second Inequality:
\[ -39 > -3x - 3 \]
1. Add 3 to both sides:
   \[
   -39 + 3 > -3x
   \]
   \[
   -36 > -3x
   \]
2. Divide by \(-3\) (again, reverse the inequality):
   \[
   \frac{-36}{-3} < x
   \]
   \[
   12 < x \quad \text{or} \quad x > 12
   \]

### Final Solution:
The inequality is \( x \leq 7 \) or \( x > 12 \). This means the solution set includes:
\[ x \in (-\infty, 7] \cup (12, \infty) \]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you solve compound inequalities?
2. What is the rule for reversing inequalities?
3. What happens when you divide by a negative number in inequalities?
4. Can inequalities have more than one solution range?
5. How do you graph the solution on a number line?

**Tip:** When solving inequalities, always remember to reverse the inequality sign if you multiply or divide by a negative number!

Learn how to solve the compound inequalities −24 ≤ −3x − 3 or −39 > −3x − 3. This step-by-step solution explains key algebraic concepts, including reversing the inequality when dividing by negative numbers, and is suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation