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.