. 1−|3p+1|=−3! Thank you

p = - , 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 = -

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 = - : 1 - | - 5 + 1 | = 1 - | - 4 | = 1 - 4 = - 3 ← true

Thus the solutions are p = 1, p = -