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

Question

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 \(-6n + 3 \geq 21\), 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: Remember that when you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign. \[ n \leq \frac{18}{-6} \] \[ n \leq -3 \]

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

Graphing the Solution:

To graph the solution \(n \leq -3\):

• Draw a number line.
• Locate the point -3 on the number line.
• Since \(n\) can be equal to -3, draw a closed (or filled) circle at -3.
• Shade to the left of -3 to indicate that all values less than -3 are included in the solution.

Description of the Graph:

The graph has a closed circle at -3 (indicating that -3 is included in the solution), and the shading extends to the left, representing all numbers less than -3. The graph visually shows that the solution encompasses all values down to negative infinity.