# How do you solve |- 3p | = 27?

Apr 12, 2018

See a solution process below:

#### Explanation:

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

Solution 1:

$- 3 p = - 27$

$\frac{- 3 p}{\textcolor{red}{- 3}} = \frac{- 27}{\textcolor{red}{- 3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 3}}} p}{\cancel{\textcolor{red}{- 3}}} = 9$

$p = 9$

Solution 2:

$- 3 p = 27$

$\frac{- 3 p}{\textcolor{red}{- 3}} = \frac{27}{\textcolor{red}{- 3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 3}}} p}{\cancel{\textcolor{red}{- 3}}} = - 9$

$p = - 9$

The Solution Set Is:

$p = \left\{- 9 , 9\right\}$

Apr 12, 2018

p = 9

#### Explanation:

The absolute value can be thought of as the distance a number is from 0 on a number line. As you can see in the image above, each point on the number line is a certain distance from 0. What we call negative and positive is entirely arbitrary, and when considering the absolute distance something is from 0 (ie the absolute value) we only care how many numbers away from 0 it is. On that number line, 5 is five numbers away from 0 on the number line, but so is -5. Thus, $\left\mid 5 \right\mid$ and $\left\mid - 5 \right\mid$ both = 5 (as they're both 5 numbers away from 0).

Now, this can be applied to your question as, no matter what p is, it is a finite number, thus -3p would be exactly as many numbers from 0 as 3p is. That is to say, $\left\mid - 3 p \right\mid = \left\mid 3 p \right\mid = 3 p$. Now, we have: 3p = 27 and we can divide both sides by 3 to get p = 9. Hence, your final answer is p = 9, as above.