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 \(-6n + 3 \geq 21\), follow these steps:

1. Subtract 3 from both sides: \[ -6n \geq 21 - 3 \] \[ -6n \geq 18 \]

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

The solution to the inequality is \(n \leq -3\).

Graph Description

On a number line, the graph of the solution will look like this:

• Draw a horizontal line representing the number line.
• Place a closed dot (or solid dot) at \(-3\) to indicate that \(-3\) is included in the solution (since the inequality is less than or equal to).
• Shade the area to the left of \(-3\) to show all numbers less than \(-3\) are included in the solution.

Overall, the graph represents all real numbers less than or equal to \(-3\).