https://file.aiquickdraw.com/mathbot/file/172775320210039uft6yg.jpg

Let's solve and graph the compound inequality provided in the image.

The compound inequality is:
\[
-12x + 11 > 83 \quad \text{or} \quad -7 + 3x \geq -4
\]

### Solving Each Inequality:
#### First Inequality:
\[
-12x + 11 > 83
\]
1. Subtract 11 from both sides:
\[
-12x > 83 - 11
\]
\[
-12x > 72
\]
2. Divide both sides by -12. (Remember to reverse the inequality sign when dividing by a negative number):
\[
x < \frac{72}{-12}
\]
\[
x < -6
\]

#### Second Inequality:
\[
-7 + 3x \geq -4
\]
1. Add 7 to both sides:
\[
3x \geq -4 + 7
\]
\[
3x \geq 3
\]
2. Divide both sides by 3:
\[
x \geq \frac{3}{3}
\]
\[
x \geq 1
\]

### Solution:
The solution is the union of both inequalities:
\[
x < -6 \quad \text{or} \quad x \geq 1
\]

### Graph:
- For \( x < -6 \), we use an open circle at \( -6 \) because it's a strict inequality.
- For \( x \geq 1 \), we use a closed circle at \( 1 \) because it's an inclusive inequality.

The graph would have two regions:
1. A line extending to the left from \( -6 \) (not including \( -6 \)).
2. A line starting from \( 1 \) (including \( 1 \)) and extending to the right.

You can graph this on a number line, with open and closed circles at the appropriate points. If you'd like assistance with the graph, let me know!

---

Would you like further details on solving inequalities or graphing?  
Here are 5 related questions to expand your understanding:
1. What happens if the inequality symbols are reversed in compound inequalities?
2. How does dividing by a negative number affect inequality signs?
3. How would you solve compound inequalities that include "and" instead of "or"?
4. What are the implications of open versus closed circles on a graph?
5. How do you handle inequalities involving absolute values?

**Tip**: Always remember to reverse the inequality sign when multiplying or dividing by a negative number in inequalities.

Solve and graph the following compound inequality: -12x + 11 > 83 or -7 + 3x ≥ -4

Learn how to solve and graph the compound inequality -12x + 11 > 83 or -7 + 3x ≥ -4. This step-by-step solution covers key algebraic concepts and teaches how to handle inequalities, including reversing the inequality sign when dividing by a negative number. Suitable for 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