https://file.aiquickdraw.com/mathbot/file/1727884017117nyc098a3.jpg

Let's solve the inequality shown in the image:

\[
5(3x - 5) < -3(-5x + 10)
\]

### Step 1: Expand both sides

First, distribute the numbers outside the parentheses on both sides.

- Left side:
\[
5(3x - 5) = 15x - 25
\]

- Right side:
\[
-3(-5x + 10) = 15x - 30
\]

The inequality becomes:
\[
15x - 25 < 15x - 30
\]

### Step 2: Simplify

Subtract \(15x\) from both sides:
\[
-25 < -30
\]

### Step 3: Analyze

At this point, we have \(-25 < -30\), which is **false**.

### Conclusion:

Since the statement is false, there are **no solutions** to the inequality. The correct answer is "No solutions."

---

Would you like more details or have any other questions? Here are 5 related questions that could expand your understanding:

1. How do you solve inequalities with variables on both sides?
2. What happens if an inequality simplifies to a true statement, like \(0 < 5\)?
3. How do you handle inequalities when multiplying or dividing by negative numbers?
4. Can you graph the solution to an inequality with no solutions?
5. What is the difference between "no solutions" and "all real numbers" as answers to inequalities?

**Tip:** When simplifying inequalities, always check if the variables cancel out, as this can lead to either no solutions or all real numbers as the solution.

Solve the inequality: 5(3x - 5) < -3(-5x + 10)

Learn how to solve the inequality 5(3x - 5) < -3(-5x + 10) using distributive properties and simplification techniques. This problem involves algebraic inequalities and is suitable for students in Grades 7-9.

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