https://file.aiquickdraw.com/mathbot/file/17266245560961nm91hb7.jpg

The inequality problem presented in the image is as follows:

\[
-2x < 18 \quad \text{or} \quad x + 5 \leq -1
\]

We will solve each part separately:

### 1. Solve \(-2x < 18\):

\[
-2x < 18
\]

To isolate \(x\), divide both sides by \(-2\). Remember, when dividing or multiplying an inequality by a negative number, the inequality sign reverses:

\[
x > \frac{18}{-2}
\]
\[
x > -9
\]

So, the solution for the first inequality is:
\[
x > -9
\]

### 2. Solve \(x + 5 \leq -1\):

\[
x + 5 \leq -1
\]

Subtract 5 from both sides:

\[
x \leq -1 - 5
\]
\[
x \leq -6
\]

So, the solution for the second inequality is:
\[
x \leq -6
\]

### 3. Final Solution:

Since the two inequalities are connected by "or", the solution is the union of the two:

\[
x > -9 \quad \text{or} \quad x \leq -6
\]

This means \(x\) can be either greater than \(-9\) or less than or equal to \(-6\), which can be expressed as:

\[
x \in (-9, \infty) \cup (-\infty, -6]
\]

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How would the solution change if the word "or" was replaced by "and"?
2. What happens if we reverse the inequality in the first part (e.g., \(-2x > 18\))?
3. Can you graph the solution set on a number line?
4. How do the rules of inequalities change when multiplying or dividing by a negative number?
5. What are the key differences in solving "or" versus "and" compound inequalities?

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

Learn how to solve the compound inequality -2x < 18 or x + 5 ≤ -1 step by step. This example covers core algebraic concepts, such as solving inequalities, reversing inequality signs when dividing by a negative number, and interpreting the union of solution sets. Suitable for students in 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