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

##### 2 Answers

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:**

**Solution 2:**

**The Solution Set Is:**

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,

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,