Solve the inequality and graph the solution on the line provided.
5, x, minus, 15, is less than or equal to, 10
5x−15≤
10

Let's solve the inequality step by step:

**Given inequality**:
\[
5x - 15 \leq 10
\]

### Step 1: Add 15 to both sides of the inequality
\[
5x - 15 + 15 \leq 10 + 15
\]
\[
5x \leq 25
\]

### Step 2: Divide both sides by 5 to isolate \( x \)
\[
x \leq \frac{25}{5}
\]
\[
x \leq 5
\]

So, the solution to the inequality is:
\[
x \leq 5
\]

### Graphing the solution on a number line:

- Draw a number line.
- Place a solid dot at \( x = 5 \) because the inequality includes "equal to" (i.e., \( \leq \)).
- Shade the line to the left of \( x = 5 \) to represent all numbers less than or equal to 5.

Would you like me to create the graph or provide more details on the solution?

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Here are 5 questions for deeper understanding:

1. What happens if we change the inequality sign to \( < \)?
2. How would the solution change if it was \( 5x - 15 \geq 10 \)?
3. What if the constant on the right-hand side was negative?
4. How would you graph the solution if the inequality was strict (i.e., no equal to)?
5. Can you solve a similar inequality like \( 4x - 12 \leq 8 \)?

**Tip**: Always check if your inequality includes "equal to" to know whether to use an open or closed dot on the number line.

Solve the inequality and graph the solution on the line provided.
5x - 15 ≤ 10

Learn how to solve the linear inequality 5x - 15 ≤ 10 and graph the solution on a number line. This step-by-step guide walks you through algebraic manipulation and graphing, suitable for students in Grades 6-8.

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