Question

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

Answer 1

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.