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To solve the inequality \( 4 > \frac{y}{-5} \) for \( y \), let's go through each step carefully:

### Step 1: Eliminate the Denominator
To isolate \( y \), start by multiplying both sides of the inequality by \(-5\). Remember that when you multiply or divide by a negative number in an inequality, you must reverse the inequality sign:

\[
4 \times (-5) < y
\]

### Step 2: Perform the Multiplication
Calculate \( 4 \times (-5) \):

\[
-20 < y
\]

### Step 3: Rewrite the Inequality
The inequality can be rewritten as:

\[
y > -20
\]

### Final Answer
The solution is:

\[
y > -20
\]

Would you like more details on these steps or have any questions?

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Here are five related questions to deepen understanding:
1. What happens to the inequality when you multiply both sides by a positive number?
2. Why do we reverse the inequality sign when multiplying by a negative number?
3. How would the inequality change if the original problem was \(4 < \frac{y}{-5}\)?
4. What is the solution if the inequality was \(4 \geq \frac{y}{-5}\)?
5. How would you graph the solution \( y > -20 \) on a number line?

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

Solve the inequality for y: 4 > y / -5. Simplify your answer as much as possible.

Learn how to solve the inequality 4 > y / -5 by isolating y. This step-by-step solution explores key algebraic concepts and demonstrates the impact of multiplying by a negative number on the inequality sign. Suitable for students in Grades 7-9.

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