https://file.aiquickdraw.com/mathbot/file/17266972305386dav1pfj.jpg

The inequality provided is:

\[
-3(x - 5) < 60
\]

### Step-by-step solution:

1. **Distribute the \(-3\)**:
   \[
   -3(x - 5) = -3x + 15
   \]
   So, the inequality becomes:
   \[
   -3x + 15 < 60
   \]

2. **Subtract 15 from both sides**:
   \[
   -3x < 60 - 15
   \]
   \[
   -3x < 45
   \]

3. **Divide by \(-3\)** on both sides, but remember to **reverse the inequality sign** when dividing by a negative number:
   \[
   x > \frac{45}{-3}
   \]
   \[
   x > -15
   \]

### Final answer:
\[
x > -15
\]

Would you like further details or have any questions?

Here are 5 related questions to explore:

1. How do you solve linear inequalities with variables on both sides?
2. What happens to the inequality symbol when dividing by a negative number?
3. How can inequalities be graphed on a number line?
4. What are the key differences between solving equations and inequalities?
5. How can inequalities be combined in compound inequality problems?

**Tip**: Always remember to reverse the inequality when multiplying or dividing both sides by a negative number.

Learn how to solve the linear inequality -3(x - 5) < 60 using the distributive property and the rule for reversing the inequality sign when dividing by a negative number. Suitable for students in Grades 7-9.

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