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

Answer 1

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

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

2. Divide by \(-6\): When dividing both sides of an inequality by a negative number, the direction of the inequality sign changes: \[ n \leq \frac{18}{-6} \] This simplifies to: \[ n \leq -3 \]

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

Graphing the Solution

To graph \(n \leq -3\) on a number line:

• Draw a number line.
• Locate the point \(-3\) on the line.
• Place a closed circle (or dot) on \(-3\) to indicate that \(-3\) is included in the solution (since it is "less than or equal to").
• Shade the line to the left of \(-3\) to indicate that all numbers less than \(-3\) are included in the solution.

Description of the Graph

• The graph contains a closed circle at \(-3\).
• It shades to the left, extending to negative infinity.
• This represents all values of \(n\) that are less than or equal to \(-3\).

In conclusion, the graph visually represents the inequality by indicating the set of all \(n\) values that satisfy \(n \leq -3\).