Let's solve the inequality \( 15 \cdot \frac{x}{15} < 8 \cdot 15 \).

1. **Simplify the left side of the inequality**:

\[
15 \cdot \frac{x}{15} = x
\]

So the inequality simplifies to:

\[
x < 8 \cdot 15
\]

2. **Multiply the numbers on the right side**:

\[
x < 120
\]

Thus, the solution to the inequality is:

\[
x < 120
\]

This means \( x \) can be any number less than 120.

Would you like more details or have any questions?

Here are five related questions:
1. How would the inequality change if it were \( 15 \cdot \frac{x}{15} > 8 \cdot 15 \)?
2. What happens if you divide both sides by 15 before simplifying?
3. How do you solve \( 15 \cdot \frac{x}{15} \leq 8 \cdot 15 \)?
4. What if the inequality were \( 15 \cdot \frac{x}{15} = 8 \cdot 15 \)?
5. Can you graph the solution \( x < 120 \) on a number line?

**Tip:** When dealing with fractions in inequalities, try simplifying them early on to make the problem easier to solve.

Learn how to solve the inequality 15 * (x / 15) < 8 * 15 with a detailed step-by-step solution. This problem covers key algebraic concepts, including inequalities. Suitable for students in Grades 7-9.

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