The inequality provided in the image is:

$2x \leq 10 \quad \text{or} \quad 3x + 1 > 3$

Let's solve each part of the inequality step by step:

1. First inequality: $2x \leq 10$

• Divide both sides by 2: $x \leq \frac{10}{2}$ $x \leq 5$

2. Second inequality: $3x + 1 > 3$

• Subtract 1 from both sides: $3x > 3 - 1$ $3x > 2$
• Divide both sides by 3: $x > \frac{2}{3}$ $x > \frac{2}{3}$

Now, we combine both inequalities using "or":

$x \leq 5 \quad \text{or} \quad x > \frac{2}{3}$

This means that $x$ can be any value less than or equal to 5, or greater than $\frac{2}{3}$. Therefore, the solution is:

$x \in (-\infty, 5] \cup \left( \frac{2}{3}, \infty \right)$

Would you like more details on any of these steps or explanations?

Here are 5 relative questions to expand on this topic:

1. How do we graph the solution set of this inequality on a number line?
2. What are the rules for solving inequalities with "or" conditions?
3. How does solving compound inequalities differ from solving systems of equations?
4. Can you explain the difference between "or" and "and" in compound inequalities?
5. How does dividing or multiplying both sides of an inequality by a negative number affect the inequality?

Tip: Always be careful when solving inequalities. If you multiply or divide both sides by a negative number, you need to reverse the inequality sign.