The problem shown in the image asks to find the values of $x$ that satisfy a given inequality, as represented by a number line.

Interpreting the Problem:

It seems the inequality is divided into different parts, indicated by the boxes and the corresponding number line. Based on the typical presentation, you're likely asked to solve an inequality that involves finding the intervals of $x$ that make the inequality true.

Given Expression:

The boxes provided appear to show two different regions on the number line that correspond to the solution of the inequality.

Steps to Solve:

1. Identify the Inequality: Determine whether you are solving for $x$ in a linear inequality or a compound inequality.
2. Solve for $x$: If it’s a compound inequality, break it into two separate inequalities.
3. Represent on Number Line: Plot the solutions on the number line, ensuring you accurately identify the type of boundary (open or closed circle).
4. Combine Solutions: If the inequality is compound, combine the solution intervals where both conditions are met.

Specific to Image:

• The image seems to display a number line with the range $-5 < x \leq 1$, with points $-5$ and $1$ being critical values.
• The interval notation that should be selected might be:
  • Open interval at $-5$ (denoted by an open circle, meaning $-5$ is not included).
  • Closed interval at $1$ (denoted by a closed circle, meaning $1$ is included).

Conclusion:

If the problem asks for the values of $x$ such that the expression is true within the indicated intervals:

• The solution set would be $x \in (-5, 1]$.

Would you like more details on any of these steps, or do you have any questions? Here are some related questions you might consider:

1. How do you solve compound inequalities algebraically?
2. What is the difference between open and closed intervals on a number line?
3. How can you check if a solution to an inequality is correct?
4. Why is it important to understand the boundary points when solving inequalities?
5. How would this problem change if one of the inequalities was strict, or if the inequality signs were reversed?

Tip: Always double-check your solution on the number line to ensure all critical points and intervals are correctly interpreted.