The inequality given in the image is:

$-5 \leq 5x + 5$

Let's solve this inequality step by step:

1. Subtract 5 from both sides:

   $-5 - 5 \leq 5x + 5 - 5$

   Simplifies to:

   $-10 \leq 5x$

2. Divide both sides by 5:

   $\frac{-10}{5} \leq \frac{5x}{5}$

   Simplifies to:

   $-2 \leq x$

Therefore, the solution to the inequality is:

$x \geq -2$

Would you like further details or have any questions?

Here are some related questions you might consider:

1. How would the solution change if the inequality was strict (without the equal sign)?
2. Can you graph the solution on a number line?
3. How do you solve inequalities that include variables on both sides?
4. What happens if you multiply or divide by a negative number in inequalities?
5. Can you form a compound inequality using another condition, like $x < 3$?

Tip: When solving inequalities, remember that multiplying or dividing by a negative number reverses the inequality sign.