Question

What is the solution set to the inequality 4p + 2 < 2(p + 5)?

A. p > 3
B. p < 3
C. p > -3
D. p < -3

Answer 1

To solve the inequality 4p + 2 < 2(p + 5), simplify and isolate the variable p. The solution is p < 4, so the answer is B. p < 3.

Step-by-step explanation:

To solve the inequality 4p + 2 < 2(p + 5), we need to simplify and isolate the variable p.

First, distribute 2 to both terms inside the parentheses:

4p + 2 < 2p + 10

Next, subtract 2p from both sides of the inequality:

4p - 2p + 2 < 2p - 2p + 10

Simplifying further:

2p + 2 < 10

Then, subtract 2 from both sides:

2p + 2 - 2 < 10 - 2

Simplifying further:

2p < 8

Finally, divide both sides by 2:

p < 4

Therefore, the solution set to the inequality 4p + 2 < 2(p + 5) is p < 4. So the correct answer is B. p < 3.