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!