What's the answer to 4|p-3|=|2p+8|? And how do you check your answer?

We want to solve 4|p-3| = |2p+8|

Ths equation is equvalent to 4 equatons.

Case 1.

4 (p - 3) = 2p + 8

4p - 12 = 2p + 8

2p = 20

Answer: p = 10

Check the solution.

4|p-3| = 4*7 = 28

|2p+8| = 2*10+8 = 28

The solution is correct.

Case 2.

4 (3 - p) = 2p + 8

12 - 4p = 2p + 8

4 = 6p

Answer: p = 2/3

Check the solution.

4|p-3| = 4*| (2/3-3) | = 28/3

|2p+8| = 28/3

The solution is correct.

Case 3.

4 (p-3) = - 2p - 8

4p - 12 = - 2p - 8

6p = 4

Answer: p = 2/3

The solution is correct because it was checked in case 2.

Case 4.

4 (3 - p) = - 2p - 8

12 - 4p = - 2p - 8

20 = 2p

Answer: p = 10

The answer s correct because t was checked in Case 1.

Answers:

p = 10 or p = 2/3.

Both answers check out to be correct.