10=43–|17p+12|
You won't use the absolute sign here. Since you cannot add variable to number AND there are no negatives.
10=43–|17p+12|
10=43–17p+12
Add 12 to 43.
10=43–17p+12
10=55-17p
Add 17p on both sides.
10=55-17p
17p+10=55
Subtract 10 from both sides.
17p+10=55
17p=45.
Therefore, the answer is p=2.64705882353.