Question

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

Answer 1

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:

`-3p = -27`

`(-3p)/color(red)(-3) = (-27)/color(red)(-3)`

`(color(red)(cancel(color(black)(-3)))p)/cancel(color(red)(-3)) = 9`

`p = 9`

Solution 2:

`-3p = 27`

`(-3p)/color(red)(-3) = 27/color(red)(-3)`

`(color(red)(cancel(color(black)(-3)))p)/cancel(color(red)(-3)) = -9`

`p = -9`

The Solution Set Is:

`p = {-9, 9}`

Answer 2

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, `abs(5)` and `abs(-5)` 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, `abs(-3p) = abs(3p) = 3p`. 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.