To solve the inequality \( 4x - 4 \leq 24 \) or \( 4x - 4 \geq 44 \), let's break it down into two parts and solve each inequality separately.

### 1. Solving \( 4x - 4 \leq 24 \):
\[
4x - 4 \leq 24
\]
Add 4 to both sides:
\[
4x \leq 28
\]
Now, divide both sides by 4:
\[
x \leq 7
\]

### 2. Solving \( 4x - 4 \geq 44 \):
\[
4x - 4 \geq 44
\]
Add 4 to both sides:
\[
4x \geq 48
\]
Now, divide both sides by 4:
\[
x \geq 12
\]

### Final Solution:
The solution to the inequality is:
\[
x \leq 7 \quad \text{or} \quad x \geq 12
\]

This means the values of \(x\) are either less than or equal to 7, or greater than or equal to 12.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. How do you solve compound inequalities involving "and" instead of "or"?
2. What happens when both inequalities have overlapping solutions?
3. How do you represent these solutions on a number line?
4. Can inequalities like this be solved graphically?
5. How does the solution change if the inequalities use strict \(<\) or \(>\) symbols?

**Tip**: Always remember to flip the inequality sign when multiplying or dividing both sides by a negative number!

Learn how to solve the linear inequalities 4x−4≤24 and 4x−4≥44 with step-by-step instructions. This solution covers essential concepts in inequalities and linear equations, suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation