To solve the inequality:

\[
5x - 15x \leq 40
\]

### Step 1: Simplify the expression.
Combine like terms on the left side:

\[
-10x \leq 40
\]

### Step 2: Solve for \(x\).
Divide both sides by \(-10\). When dividing by a negative number in an inequality, remember to **flip the inequality sign**:

\[
x \geq \frac{40}{-10}
\]

\[
x \geq -4
\]

### Solution:
The solution to the inequality is:

\[
x \geq -4
\]

Would you like any further clarification or additional examples?

Here are five related questions to expand your understanding:
1. What if the inequality were \(5x - 15x \geq 40\)? How would that change the solution?
2. Can you graph the solution on a number line?
3. How would you solve the inequality if there were other terms on both sides?
4. What happens if the inequality includes fractions or decimals?
5. How does dividing by a negative number affect an inequality, and why?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing both sides by a negative number in inequalities!

Learn how to solve the linear inequality 5x - 15x ≤ 40 with a detailed step-by-step guide. This solution simplifies the inequality, explains the importance of flipping the inequality sign when dividing by a negative number, and is suitable for students in Grades 6-8.

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