https://file.aiquickdraw.com/mathbot/file/1728852668865yn6irx4b.jpg

Let me help you by solving the inequalities one by one from your image. I will go through each question systematically, ensuring the process and solution are clear. Let's start with a few of them.

### 11. \( 3x + 5 > -4 \)

**Step 1:** Subtract 5 from both sides:
\[
3x > -4 - 5
\]
\[
3x > -9
\]

**Step 2:** Divide both sides by 3:
\[
x > -3
\]

### 12. \( 2x + 1 > -1 \)

**Step 1:** Subtract 1 from both sides:
\[
2x > -1 - 1
\]
\[
2x > -2
\]

**Step 2:** Divide both sides by 2:
\[
x > -1
\]

### 13. \( 5 - 6y < -1 \)

**Step 1:** Subtract 5 from both sides:
\[
-6y < -1 - 5
\]
\[
-6y < -6
\]

**Step 2:** Divide both sides by -6 (and reverse the inequality):
\[
y > 1
\]

### 14. \( 7 - 9y > 43 \)

**Step 1:** Subtract 7 from both sides:
\[
-9y > 43 - 7
\]
\[
-9y > 36
\]

**Step 2:** Divide both sides by -9 (and reverse the inequality):
\[
y < -4
\]

### 15. \( 6 - a \leq 6 \)

**Step 1:** Subtract 6 from both sides:
\[
-a \leq 6 - 6
\]
\[
-a \leq 0
\]

**Step 2:** Multiply both sides by -1 (and reverse the inequality):
\[
a \geq 0
\]

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These are the solutions for the first five inequalities. Would you like me to continue solving the rest? Let me know if you have any questions on the steps or concepts. Here's how to extend your understanding:

1. How do we handle inequalities when dividing or multiplying by negative numbers?
2. Why do we reverse the inequality sign when dividing by a negative number?
3. What are the real-world applications of solving linear inequalities?
4. Can you write the solution sets for these inequalities on a number line?
5. How would the solution change if we changed the inequality signs to "less than or equal to"?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing by a negative number.

Learn how to solve linear inequalities like '3x + 5 > -4' and more. These problems cover core algebraic concepts such as isolating variables, rational expressions, and handling inequalities. Ideal for students in Grades 9-10.

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