Question

Solve and graph the solution to the inequality −6n+3≥21 on your own paper or device. In the box below, give the solution to the inequality and describe how your graph looks.(2 points)

Answer 1

To solve the inequality \(-6n + 3 \geq 21\), we can follow these steps:

1. **Isolate the variable term**:
\(-6n + 3 \geq 21\)

Subtract 3 from both sides:
\(-6n \geq 21 - 3\)

Simplifying the right side:
\(-6n \geq 18\)

2. **Divide by -6**:
Since we are dividing by a negative number, we must reverse the inequality:
\(n \leq \frac{18}{-6}\)

This simplifies to:
\(n \leq -3\)

So, the solution to the inequality is:
\[
n \leq -3
\]

### Graphing the Solution

On a number line:

- Draw a horizontal line that represents the number line.
- Mark -3 on the number line.
- Since the inequality is "less than or equal to," we use a closed dot at -3 to indicate that -3 is included in the solution.
- Shade everything to the left of -3 to represent all numbers less than -3.

### Description of the Graph

The graph of the inequality would show a closed dot at -3 with a shaded line extending to the left, indicating all values that are less than or equal to -3 are part of the solution set.