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To solve the inequality:

\[
-5(x + 5) + 26 \leq 2(8 - x)
\]

### Step-by-Step Solution:

1. **Distribute** the terms within the parentheses:
   \[
   -5(x + 5) = -5x - 25
   \]
   \[
   2(8 - x) = 16 - 2x
   \]

   Substituting these into the inequality, we get:
   \[
   -5x - 25 + 26 \leq 16 - 2x
   \]

2. **Combine like terms** on the left side:
   \[
   -5x + 1 \leq 16 - 2x
   \]

3. **Move all terms involving \( x \) to one side** and constants to the other side:
   - Add \( 2x \) to both sides:
     \[
     -5x + 2x + 1 \leq 16
     \]
     \[
     -3x + 1 \leq 16
     \]

   - Subtract 1 from both sides:
     \[
     -3x \leq 15
     \]

4. **Divide by -3** and reverse the inequality sign (since dividing by a negative number reverses the inequality):
   \[
   x \geq -5
   \]

### Final Answer:
\[
x \geq -5
\]

Would you like further details on any of these steps, or do you have any questions?

---

Here are some additional questions related to this topic:

1. How would you solve a similar inequality if there were absolute values involved?
2. What would change if the inequality symbol were \( < \) instead of \( \leq \)?
3. How would the solution change if there were no negative signs on the variable terms?
4. Can you graph the solution \( x \geq -5 \) on a number line?
5. What is the impact of multiplying or dividing both sides by zero in an inequality?

**Tip:** Always remember to reverse the inequality sign when you multiply or divide by a negative number in inequalities.

Solve the inequality for x: -5(x + 5) + 26 ≤ 2(8 - x). Simplify your answer as much as possible.

Learn how to solve the inequality -5(x + 5) + 26 ≤ 2(8 - x) with a step-by-step solution. This problem covers key algebraic concepts such as the distributive property, combining like terms, and properties of inequalities. Suitable for students in Grades 9-10.

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