Question

1. solve the inequality and graph the solution.

6 ≥ 3p
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.
(number line with marks at 0,1,2,3,4,5,6,7)

Explanation:

Step1: Divide both sides by 3

To solve the inequality \( 6 \geq 3p \), we divide both sides by 3 (since 3 is positive, the inequality sign remains the same). So we have \( \frac{6}{3} \geq \frac{3p}{3} \).

Step2: Simplify both sides

Simplifying the left side \( \frac{6}{3}=2 \) and the right side \( \frac{3p}{3}=p \). So the inequality becomes \( 2 \geq p \) or \( p \leq 2 \).

For graphing: We plot a closed dot at 2 (because the inequality is "less than or equal to", so 2 is included) and draw an arrow to the left (towards negative infinity) to represent all numbers less than or equal to 2.

Answer:

The solution to the inequality \( 6 \geq 3p \) is \( p \leq 2 \). For the graph, there is a closed endpoint at 2 with an arrow pointing to the left along the number line.