Question

What is -6>=-p+4p where is it graphed on the number line.

A. p≤−3
B. p≥−3
C.p≤3
D.p≥3

Answer 1

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.