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!

Learn how to solve the inequality 3(-5 - x) + x < -10 - x with a detailed step-by-step solution. This problem covers key algebra concepts such as the distributive property, combining like terms, and solving inequalities. Suitable for students in Grades 7-10.

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