https://file.aiquickdraw.com/mathbot/file/1726253660755bedylu32.jpg

The question in the image asks for a value of \(x\) that is within 4 units of 15. Let's break it down step by step:

### Part (a):
You need to think of some values of \(x\) that are within 4 units of 15. This means that \(x\) must be between 11 and 19, because 4 units away from 15 on either side would be:
\[
15 - 4 = 11 \quad \text{and} \quad 15 + 4 = 19
\]
So, some values that meet this constraint would be numbers like 12, 13, 16, 18, etc.

### Part (b):
Now, you're asked to write an inequality that represents **all** values of \(x\) that meet this constraint. The distance from \(x\) to 15 must be less than or equal to 4 units. This can be written as:
\[
|x - 15| \leq 4
\]
This absolute value inequality means that \(x\) must be within 4 units of 15, both above and below.

### Part (c):
To solve the absolute value inequality, we can rewrite it as a compound inequality:
\[
11 \leq x \leq 19
\]
So, on the number line, all values of \(x\) between 11 and 19 (inclusive) will meet this constraint. You would draw a closed interval on the number line from 11 to 19, indicating that both endpoints are included.

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Would you like further details or explanations about this problem? Here are some related questions to deepen understanding:

1. What happens if we change the value of 4 units to a different number, such as 6 units?
2. How do we graph absolute value inequalities on a number line?
3. Can we solve more complex absolute value inequalities, like \( |x - 7| \geq 3 \)?
4. What is the meaning of the solution to an absolute value inequality?
5. How would this problem change if the inequality was strict (i.e., \( |x - 15| < 4 \))?

**Tip:** Absolute value inequalities often translate to two separate inequalities and can be interpreted as distances on a number line!

Suppose we want to choose a value of x within 4 units of 15. [This means a value of x that is less than 4 units away from 15.] a. Think about some values of x that meet this constraint. b. Write an inequality that represents all values of x that meet this constraint. c. On the number line below, represent all values of x that meet this constraint.

Learn how to solve absolute value inequalities like |x - 15| ≤ 4, which means that x must be within 4 units of 15. This problem covers key algebraic concepts like inequalities and absolute values. Suitable for students in Grades 7-9.

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