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The inequality given is:

\[
-2x + 5 \leq 15
\]

### Step-by-step solution:

1. **Isolate the variable term**:
   Subtract 5 from both sides of the inequality:
   \[
   -2x + 5 - 5 \leq 15 - 5
   \]
   Simplifying:
   \[
   -2x \leq 10
   \]

2. **Solve for \( x \)**:
   Divide both sides of the inequality by \(-2\). **Note**: When dividing by a negative number, the inequality sign must be reversed.
   \[
   x \geq \frac{10}{-2}
   \]
   Simplifying:
   \[
   x \geq -5
   \]

### Final solution:

The solution set in interval notation is:
\[
[-5, \infty)
\]

This means that \(x\) can take any value greater than or equal to \(-5\).

---

Do you want more details or have any questions?

Here are 5 related questions to consider:
1. How do you handle inequalities when multiplying or dividing by negative numbers?
2. What is the significance of reversing the inequality sign?
3. Can you graph the solution set of this inequality on a number line?
4. How would the solution change if the inequality was strict (i.e., \( < \) instead of \( \leq \))?
5. What are common errors students make when solving inequalities?

**Tip**: Always remember to reverse the inequality sign when multiplying or dividing by a negative number.

Solve the inequality. Write the solution set in interval notation: -2x + 5 ≤ 15.

Learn how to solve the inequality -2x + 5 ≤ 15 step-by-step and write the solution in interval notation. Understand key concepts like isolating the variable, and reversing the inequality sign when dividing by a negative number. Suitable for students in Grades 7-10.

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