Final answer:
The inequality -6 ≥ -p + 4p simplifies to p ≤ -2, meaning the correct answer is A. p ≤ -3. The solution is graphed on a number line with a filled circle at -2 and shading to the left.
Step-by-step explanation:
The question asks to solve the inequality -6 ≥ -p + 4p and to determine where the solution is graphed on the number line. Combine the terms on the right to simplify the inequality:
-6 ≥ 3p
Divide both sides by 3 to find the value of p:
p ≤ -2
This tells us that the value of p must be less than or equal to -2. Therefore, the correct answer is A. p ≤ -3. When this is graphed on a number line, the line extends from minus infinity to -2, and includes the point -2, shown by a filled circle on -2 and shading the line to the left.
To graph this inequality, draw a horizontal number line and label it with an appropriate scale. Place a filled circle at the point corresponding to p = -2 to represent that -2 is included in the solution set (since the inequality sign is '≤'). Finally, shade the part of the number line to the left of -2 to indicate all the values of p that satisfy the inequality.