How do I solve |5-3p|+9=13p+8

p = - 2/5 or 3/8

Step-by-step explanation:

|5 - 3p| + 9 = 13p + 8

|5 - 3p| = 13p - 1

If 5 - 3p is positive:

5 - 3p = 13p - 1

6 = 16p

p = 3/8

If 5 - 3p is negative:

- (5 - 3p) = 13p - 1

-5 + 3p = 13p - 1

-4 = 10p

p = - 2/5

Alternatively, we can square both sides of the equation:

(5 - 3p) ² = (13p - 1) ²

25 - 30p + 9p² = 169p² - 26p + 1

0 = 160p² + 4p - 24

0 = 40p² + p - 6

0 = (5p + 2) (8p - 3)

p = - 2/5 or 3/8