Solve and graph the solution to the inequality −6n+3≥21

Question

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

Answer 1

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

1. Isolate the term with \(n\): \[ -6n + 3 \geq 21 \] Subtract 3 from both sides: \[ -6n \geq 21 - 3 \] \[ -6n \geq 18 \]

2. Divide by -6: When dividing or multiplying both sides of an inequality by a negative number, we must reverse the inequality sign: \[ n \leq \frac{18}{-6} \] \[ n \leq -3 \]

Solution

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

Graphing the Solution

To graph this solution on a number line:

1. Draw a horizontal line (representing the number line).
2. Identify the point -3. Since the solution is \(n \leq -3\), we need to indicate that -3 is included in the solution.
3. Use a closed circle or solid dot at -3 to show that -3 is part of the solution.
4. Shade the line to the left of -3 to represent all numbers less than -3.

Description of the Graph

The graph will have a closed circle at -3 and shading extending to the left, indicating all values that are less than or equal to -3 are part of the solution.