Brice K.

asked • 09/28/17

Absolute values equation

and before we start, i have been told numerous times it's impossible, but why? and i find it hard to believe that.
 
I know that apparently an absolute value can't be negative,
like for example | X-3| =-4

but why can't I just do this:

| X-3| =-4
+4 to both sides so that the equation now looks like this:


| X-3|+4 =0

Arturo O.

By DEFINITION, an absolute value is always ≥ 0, because it indicates how far along the number line a particular number is from 0, regardless of whether it is to the left of 0 or to the right of 0.  A negative absolute value is logically impossible, just like a square circle or a triangle with 4 sides.
Report

09/28/17

Arturo O.

I should add that the final equation you wrote has no solution, as Michael pointed out.  You can write anything, but it can be a logical impossibility and have no solution, real or complex.
Report

09/28/17

1 Expert Answer

By:

Michael A. answered • 09/28/17

Tutor
5.0 (2,591)

Full-Time Test Prep Strategist, Algebra Instructor, Math Tutor
About this tutor ›
About this tutor ›
What positive number could you possibly add to four and obtain zero? None. The absolute value function will always return a non-negative number.
Upvote • 1 Downvote
More
Report

Brice K.

but i feel like there should be an answer somehow or is this like how you can't divide 4 by 0?
Report

09/28/17

Arturo O.

Division by 0 leads to illogical results.  For example,
 
4 x 0 = 3 x 0  [TRUE]
 
Now divide by 0 on both sides.  The 0's cancel and you get
 
4 = 3  [FALSE]
 
So you see that you cannot divide by 0, and similarly, you cannot have a negative absolute value.
Report

09/28/17

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.