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.