4y+2 less than or equal to 10 or 2y-6 > -12

The given inequality is:

\[
4y + 2 \leq 10 \quad \text{or} \quad 2y - 6 > -12
\]

Let's solve each part of the inequality separately:

### 1. Solving \( 4y + 2 \leq 10 \):
\[
4y + 2 \leq 10
\]
Subtract 2 from both sides:
\[
4y \leq 8
\]
Divide by 4:
\[
y \leq 2
\]

### 2. Solving \( 2y - 6 > -12 \):
\[
2y - 6 > -12
\]
Add 6 to both sides:
\[
2y > -6
\]
Divide by 2:
\[
y > -3
\]

### Final solution:
We now combine the two results using "or":
\[
y \leq 2 \quad \text{or} \quad y > -3
\]

This means that \( y \) can be any number greater than \(-3\) or less than or equal to 2. Therefore, the solution set is:
\[
y > -3
\]

This is because any \( y \) greater than \(-3\) will satisfy at least one part of the inequality.

Do you want more details or have any questions?

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Here are 5 related questions:
1. How do we solve compound inequalities involving both "and" and "or"?
2. What happens if the inequality involves fractions?
3. How do we graph the solution set of an inequality?
4. How would the solution change if the inequality symbols were reversed?
5. What are some real-life applications of inequalities?

**Tip:** When solving inequalities, remember to reverse the inequality sign if you multiply or divide by a negative number!

4y + 2 less than or equal to 10 or 2y - 6 > -12

Explore how to solve the compound inequality 4y + 2 ≤ 10 or 2y - 6 > -12. This step-by-step solution covers key algebraic concepts, including solving linear inequalities and understanding the properties of inequalities. Ideal for students in Grades 7-9 looking to strengthen their algebra skills.

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