Solve for p.

Question

6 = |p + 9|

Write your answers as integers or as proper or improper fractions in simplest form.

p =
or p =

Answer 1

To solve the equation \( 6 = |p + 9| \), we need to consider the two cases that arise from the absolute value.

Case 1: \[ p + 9 = 6 \] Subtracting 9 from both sides gives: \[ p = 6 - 9 \] \[ p = -3 \]

Case 2: \[ p + 9 = -6 \] Subtracting 9 from both sides gives: \[ p = -6 - 9 \] \[ p = -15 \]

Thus, the solutions are: \[ p = -3 \quad \text{or} \quad p = -15 \]

In conclusion: \[ p = -3 \text{ or } p = -15 \]