Answer:
p = - [tex]\frac{5}{3}[/tex], p = 1
Step-by-step explanation:
Given
1 - | 3p + 1 | = - 3 ( subtract 1 from both sides )
- | 3p + 1 | = - 4 ( multiply both sides by - 1 )
| 3p + 1 | = 4
The absolute value function always returns a positive value, however, the expression inside can be positive or negative, thus
3p + 1 = 4 OR - (3p + 1) = 4
Subtract 1 from both sides
3p = 3 ( divide both sides by 3 )
p = 1
OR
- (3p + 1) = 4, that is
- 3p - 1 = 4 ( add 1 to both sides )
- 3p = 5 ( divide both sides by - 3 )
p = - [tex]\frac{5}{3}[/tex]
As a check
Substitute these values into the left side of the equation and if equal to the right side then they are the solutions
p = 1 : 1 - | 3 + 1 | = 1 - |4| = 1 - 4 = - 3 ← true
p = - [tex]\frac{5}{3}[/tex] : 1 - | - 5 + 1 | = 1 - | - 4 | = 1 - 4 = - 3 ← true
Thus the solutions are p = 1, p = - [tex]\frac{5}{3}[/tex]
