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The image you uploaded contains a mathematical problem asking to solve an inequality. The specific inequality appears to be \( \frac{1}{2} (2x - 5) \leq x - 2.5 \).

Let's solve this step by step:

### Step 1: Distribute and Simplify
Start by distributing the \( \frac{1}{2} \) on the left side of the inequality:

\[
\frac{1}{2} \times (2x - 5) = \frac{1}{2} \times 2x - \frac{1}{2} \times 5 = x - 2.5
\]

So the inequality becomes:

\[
x - 2.5 \leq x - 2.5
\]

### Step 2: Subtract \( x \) from Both Sides
Now, subtract \( x \) from both sides of the inequality:

\[
x - 2.5 - x \leq x - 2.5 - x
\]

This simplifies to:

\[
-2.5 \leq -2.5
\]

### Step 3: Interpret the Result
The inequality \( -2.5 \leq -2.5 \) is always true since both sides are equal. This means that the inequality holds for all values of \( x \).

### Final Answer:
The solution to the inequality is **all real numbers**.

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Do you want more details on this solution, or have any questions?

Here are five related questions to consider:

1. What happens when solving inequalities that involve dividing by a negative number?
2. How do you solve compound inequalities?
3. How would the solution change if the inequality was strict, e.g., \( < \) instead of \( \leq \)?
4. Can you solve a quadratic inequality? What steps are involved?
5. How would you graph the solution set of this inequality on a number line?

**Tip:** Always check the final solution by substituting a value of \( x \) back into the original inequality to verify it holds true.

Solve the inequality \( \frac{1}{2} (2x - 5) \leq x - 2.5 \).

Learn how to solve the linear inequality \( \frac{1}{2} (2x - 5) \leq x - 2.5 \) step-by-step. This problem explores key algebraic concepts including distribution and properties of inequalities. Suitable for students in Grades 8-10.

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