solve the inequality for y -9/2y≤6 simplifly your answer as much as possible

To solve the inequality \(-\frac{9}{2}y \leq 6\), follow these steps:

### Step 1: Isolate \(y\) on one side of the inequality.
Start by multiplying both sides of the inequality by \(-2/9\) to eliminate the fraction. When you multiply by a negative number, you must reverse the inequality sign.

\[
y \geq 6 \times \left( -\frac{2}{9} \right)
\]

### Step 2: Simplify the right-hand side.
\[
y \geq 6 \times \left( -\frac{2}{9} \right) = -\frac{12}{9} = -\frac{4}{3}
\]

### Final Answer:
\[
y \geq -\frac{4}{3}
\]

### Solution:
The inequality simplifies to:
\[
y \geq -\frac{4}{3}
\]

Would you like more details, or do you have any questions?

Here are 5 questions to explore further:
1. How do you handle inequalities when multiplying or dividing by negative numbers?
2. What would happen if we had a greater than sign instead of less than?
3. Can this inequality be graphed on a number line?
4. What are the real-world applications of solving inequalities?
5. How does solving linear equations differ from inequalities?

**Tip:** Always remember to flip the inequality when multiplying or dividing by a negative number!

solve the inequality for y -9/2y≤6 simplify your answer as much as possible

Learn how to solve the inequality -9/2y ≤ 6 with detailed steps. This algebra problem involves key concepts such as inequalities and the rule of flipping the inequality sign when multiplying by negative numbers. Ideal for students in Grades 8-10.

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