Question

-6y>24
which operation should be used to solve the inequality

and how is it graphed

Answer 1

To solve the inequality \(-6y > 24\), you need to isolate \(y\) by performing the same operations on both sides. Here are the steps:

1. **Divide both sides by -6**: When you divide or multiply both sides of an inequality by a negative number, you must **reverse the inequality sign**.

\[
-6y > 24
\]
Dividing both sides by -6:
\[
y < -4
\]

So the operation you should use is **division by -6**, with a reversal of the inequality sign.

### Graphing the Inequality \(y < -4\)

1. **Draw a number line**: Start by drawing a horizontal line and marking several points on it, including the integer -4.

2. **Open circle on -4**: Since the inequality is \(<\) (not \(\leq\)), you put an open circle at -4 to indicate that -4 is NOT included in the solution set.

3. **Shade the region to the left of -4**: Since \(y\) is less than -4, you shade the line to the left of -4 to indicate all values of \(y\) that satisfy the inequality.

### Summary
- The operation used is **division by -6**, with the inequality sign reversed.
- The graph has an open circle at -4 and shading to the left.