We are given two inequalities to solve for \( x \):

1. \( 5x - 2 > -42 \)
2. \( 5x - 2 < 43 \)

### Solving the first inequality:
\[
5x - 2 > -42
\]
Add 2 to both sides:
\[
5x > -40
\]
Now, divide both sides by 5:
\[
x > -8
\]

### Solving the second inequality:
\[
5x - 2 < 43
\]
Add 2 to both sides:
\[
5x < 45
\]
Now, divide both sides by 5:
\[
x < 9
\]

### Combined result:
The solution is:
\[
-8 < x < 9
\]
This means \( x \) is greater than \( -8 \) and less than \( 9 \).

Would you like more details or have any questions?

### Related questions:
1. How would the solution change if the inequality symbols were reversed?
2. How do you graph the solution on a number line?
3. What happens if there are different coefficients for \( x \) in each inequality?
4. How would the solution change if it were a compound inequality with "and" instead of "or"?
5. Can you solve similar inequalities with absolute values?

### Tip:
When solving inequalities, remember that multiplying or dividing by a negative number reverses the inequality sign.

Learn how to solve the linear inequalities 5x - 2 > -42 and 5x - 2 < 43 with step-by-step explanations. This problem covers core algebraic concepts, including inequality solution techniques and the properties of inequalities. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation