https://file.aiquickdraw.com/mathbot/file/17274355776611rs87zvi.jpg

The inequality in the image reads:

\[
|x + 5| \leq 10
\]

This is an absolute value inequality. To solve this inequality, we follow these steps:

### Step 1: Remove the absolute value
For any inequality of the form \( |A| \leq B \), we rewrite it as:

\[
- B \leq A \leq B
\]

In this case:

\[
-10 \leq x + 5 \leq 10
\]

### Step 2: Solve the inequality
Now, we solve for \(x\) by isolating it in the middle part of the inequality.

- Subtract 5 from all three parts:

\[
-10 - 5 \leq x \leq 10 - 5
\]

\[
-15 \leq x \leq 5
\]

### Final Answer:
The solution to the inequality is:

\[
-15 \leq x \leq 5
\]

### Interval Notation:
The solution can be written in interval notation as:

\[
x \in [-15, 5]
\]

Would you like further details or clarifications?

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Here are 5 related questions to extend your understanding:
1. How would the solution change if the inequality was \( |x + 5| < 10 \)?
2. What happens if we solve the inequality \( |x + 5| \geq 10 \)?
3. How would you solve an inequality of the form \( |x - 3| \leq 7 \)?
4. Can you graph the solution \( -15 \leq x \leq 5 \) on a number line?
5. How would the steps change if it were \( |x - 5| \leq 10 \)?

**Tip:** When solving absolute value inequalities, always remember to break them down into two cases: one for the positive side and one for the negative side!

Learn how to solve the absolute value inequality |x + 5| ≤ 10. This solution covers algebraic concepts including absolute value inequalities, using the rule -B ≤ A ≤ B. Suitable for students in Grades 8-10.

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