−*x*−8≤−15and

−18≤−*x*−8

We have two inequalities here:

1. \(-x - 8 \leq -15\)
2. \(-18 \leq -x - 8\)

### Solving the first inequality: 
\[
-x - 8 \leq -15
\]
Add 8 to both sides:
\[
-x \leq -7
\]
Multiply both sides by \(-1\) (and remember to reverse the inequality):
\[
x \geq 7
\]

### Solving the second inequality:
\[
-18 \leq -x - 8
\]
Add 8 to both sides:
\[
-10 \leq -x
\]
Multiply both sides by \(-1\) (and reverse the inequality):
\[
x \leq 10
\]

### Combining the results:
We have:
\[
7 \leq x \leq 10
\]
So, the solution is \(x \in [7, 10]\).

Would you like more details, or have any questions?

### Related Questions:
1. How do you solve compound inequalities involving more than two inequalities?
2. Can compound inequalities be represented graphically on a number line?
3. How do you handle inequalities when dealing with fractions?
4. What happens when inequalities involve absolute values?
5. How do inequalities change when multiplying or dividing by negative numbers?

### Tip:
When solving inequalities, always remember to reverse the inequality sign when multiplying or dividing by a negative number!

−x − 8 ≤ −15 and −18 ≤ −x − 8

This page explains how to solve the compound inequality −x − 8 ≤ −15 and −18 ≤ −x − 8 step by step. Learn the process of adding, subtracting, and reversing inequalities when dealing with negative numbers. The final solution is x ∈ [7, 10], 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