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.