Let's solve the inequality $3(-5 - x) + x < -10 - x$.

Step 1: Distribute the $3$ on the left side

$3(-5 - x) = 3(-5) + 3(-x) = -15 - 3x$ So, the inequality becomes: $-15 - 3x + x < -10 - x$

Step 2: Combine like terms on both sides

On the left side, $-3x + x = -2x$, so the inequality is now: $-15 - 2x < -10 - x$

Step 3: Add $15$ to both sides to simplify

$-2x < -10 - x + 15$ $-2x < 5 - x$

Step 4: Add $x$ to both sides

$-2x + x < 5$ $-x < 5$

Step 5: Divide by $-1$ and reverse the inequality

$x > -5$

Final Solution:

The solution to the inequality is: $x > -5$

Would you like more details on any step, or do you have further questions?

Here are 5 related questions to explore:

1. How do you solve inequalities with fractions?
2. What happens if you multiply or divide by a negative number in inequalities?
3. Can you graph the solution $x > -5$ on a number line?
4. How would this change if the inequality were $\leq$ instead of $<$?
5. How can inequalities be applied in real-world problems?

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