https://file.aiquickdraw.com/mathbot/file/1729143027941d65mikmb.jpg

Let's solve some of these inequalities step by step. I'll start with problem 2 from the image. If you have a particular one you'd like to focus on, let me know!

### Problem 2:
\[
\frac{x + 4}{3} \leq \frac{1}{2}
\]

#### Step 1: Eliminate the fraction by multiplying both sides by 3:
\[
x + 4 \leq \frac{1}{2} \times 3 = \frac{3}{2}
\]

#### Step 2: Subtract 4 from both sides:
\[
x \leq \frac{3}{2} - 4
\]
\[
x \leq \frac{3}{2} - \frac{8}{2} = -\frac{5}{2}
\]

Thus, the solution in **interval notation** is:
\[
(-\infty, -\frac{5}{2}]
\]

---

Let me know if you'd like to go through another problem or need details for this one. Here are 5 possible related questions:

1. Would you like to solve problem 4 next?
2. How would the solution change if the inequality were strict (i.e., \(<\) instead of \(\leq\))?
3. Can you explain how to convert the inequality into interval notation?
4. What is the effect of multiplying or dividing by a negative number in inequalities?
5. Would you like to go through how to check the solution graphically?

**Tip:** When solving inequalities, remember that multiplying or dividing by a negative number reverses the inequality sign!

Solve the linear inequalities below and give your answer in interval notation.

Learn how to solve linear inequalities and represent the solutions using interval notation. This guide walks through step-by-step methods for solving inequalities, covering key concepts like algebraic manipulation and understanding interval notation. Perfect for students in Grades 7-10.

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