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

2 Answers
Apr 12, 2018

See a solution process below:


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}#

Apr 12, 2018

p = 9


The absolute value can be thought of as the distance a number is from 0 on a number line.

enter image source here
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.