Question

What is the solution to the inequality (-6 ≥ -p+4p), and where does its graph lie?

a) (p ≤ 2) ; Line in the plane
b) (p ≥ 2) ; Line in the plane
c) (p ≤ -2) ; Line in the plane
d) (p ≥ -2) ; Line in the plane

Answer 1

The solution to the inequality -6 ≥ -p+4p is p ≥ -2, and its graph is a solid horizontal line at p = -2, with the shaded area to the right of the line.

Step-by-step explanation:

To solve the inequality -6 ≥ -p+4p, we need to simplify the expression first. combining like terms, we have -6 ≥ 3p. Next, we isolate the variable p by dividing both sides of the inequality by 3, giving us -2 ≥ p. This means that any value of p that is greater than or equal to -2 will satisfy the inequality.

The graph of the inequality will be a horizontal line at p = -2. Since the inequality includes an equal sign, the line will be solid. The shaded area will lie to the right of the line, indicating that any value of p that is greater than or equal to -2 will be a solution.