Question

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

Answer 1

To solve the inequality \(-6n + 3 \geq 21\), let's follow these steps:

1. **Isolate the Variable**:
We want to isolate \(n\). Start by subtracting 3 from both sides of the inequality.
\[
-6n + 3 - 3 \geq 21 - 3
\]
This simplifies to:
\[
-6n \geq 18
\]

2. **Divide by \(-6\)**:
Next, we divide both sides of the inequality by \(-6\). Remember that when you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality symbol.
\[
n \leq \frac{18}{-6}
\]
Simplifying this gives:
\[
n \leq -3
\]

3. **Solution**:
The solution to the inequality is:
\[
n \leq -3
\]

4. **Graphing the Solution**:
To graph the solution on a number line:
- Draw a number line with enough space to include \(-3\).
- Place a solid dot on \(-3\) to indicate that \(-3\) is included in the solution.
- Shade the line to the left of \(-3\) to show that all numbers less than or equal to \(-3\) are part of the solution.

### Summary:
The solution to the inequality is \(n \leq -3\), and on the graph, you will have a solid dot at \(-3\) and shading to the left, indicating that all values lesser than or equal to \(-3\) satisfy the inequality.