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.

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!