https://file.aiquickdraw.com/mathbot/file/17303463146761pyfzlgt.jpg

To solve the compound inequality given:

\[
-13 \leq -x - 7 \quad \text{or} \quad -16 \geq -x - 7
\]

we’ll solve each inequality separately for \( x \), then determine the solution set.

### Step 1: Solve the first inequality
\[
-13 \leq -x - 7
\]
Add 7 to both sides:
\[
-6 \leq -x
\]
Divide by -1 (remember to reverse the inequality):
\[
6 \geq x \quad \text{or} \quad x \leq 6
\]

### Step 2: Solve the second inequality
\[
-16 \geq -x - 7
\]
Add 7 to both sides:
\[
-9 \geq -x
\]
Divide by -1 (again, reversing the inequality):
\[
9 \leq x \quad \text{or} \quad x \geq 9
\]

### Step 3: Combine the solutions
Since this is an "or" inequality, the solution set includes values of \( x \) that satisfy either inequality:
\[
x \leq 6 \quad \text{or} \quad x \geq 9
\]

### Solution in Inequality Notation
The solution in inequality notation is:
\[
x \leq 6 \quad \text{or} \quad x \geq 9
\]

### Solution on the Number Line
To represent this on the number line:
- Draw a closed circle at \( x = 6 \) and shade to the left to represent \( x \leq 6 \).
- Draw a closed circle at \( x = 9 \) and shade to the right to represent \( x \geq 9 \).

Let me know if you need more details on graphing, or have other questions! Here are some related questions to deepen understanding:

1. How would the solution change if it were an "and" compound inequality instead of "or"?
2. What happens to the inequality when dividing by a negative number, and why?
3. How can you verify the solution to a compound inequality?
4. What is the difference between open and closed circles on a number line?
5. How would the answer look different if one of the inequalities was strict (e.g., \( < \) instead of \( \leq \))?

**Tip:** Always remember to reverse the inequality sign when you multiply or divide by a negative number.

Solve for x and graph the solution on the number line below: -13 ≤ -x - 7 or -16 ≥ -x - 7

Learn how to solve the compound inequality -13 ≤ -x - 7 or -16 ≥ -x - 7 and graph the solution on a number line. This problem involves core algebraic concepts, such as inequality solving and reversal of signs when dividing by negative values. 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