Question

solve the inequality - 3p + 8 ≥ 2 and graph the solution. plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Solve the inequality for p

Subtract 8 from both sides of -3p + 8 ≥ 2.
-3p+8 - 8≥2 - 8, which simplifies to -3p≥ - 6.

Step2: Isolate p

Divide both sides by - 3. When dividing an inequality by a negative number, the direction of the inequality sign changes. So, $\frac{-3p}{-3}\leq\frac{-6}{-3}$, resulting in p ≤ 2.

Step3: Graph the solution

On the number - line, plot a closed circle at 2 (because the inequality is ≤, indicating that 2 is included in the solution set) and draw a ray to the left of 2 to represent all the values of p that satisfy the inequality.

Answer:

The solution of the inequality is p ≤ 2. On the number - line, there is a closed circle at 2 and a ray extending to the left.