Find All X Values Satisfying the Equation (Absolute Value)

NK8485

New member
Joined
Aug 25, 2015
Messages
8
I'm working on some algebra homework and am a little stumped by this one problem.

It is asking for all x-values that satisfy the equation.

I understand the concept of absolute values, so far the problems have been:

lxl=5 to which I answered: x=-5,5

lx-3l=7 ; x=-4,10.

Now I'm on the problem:
ly-3l=8-ly-3l

I'm not sure if there is a way to do this as a formula or if it's just trial and error of plugging in different numbers to see if they would work out.
 

stapel

Super Moderator
Staff member
Joined
Feb 4, 2004
Messages
15,943
Now I'm on the problem:
ly-3l=8-ly-3l

I'm not sure if there is a way to do this as a formula or if it's just trial and error...
Notice that the two absolute-value expressions are the same: y - 3. So you've got two cases: y < 3 and y > 3. Consider the cases separately:

. . .y < 3:

. . . . .y - 3 < 0
. . . . .|y - 3| = -(y - 3) = 3 - y
. . . . .8 - |y - 3| = 8 - (3 - y) = 5 + y

Then the equation becomes:

. . . . .3 - y = 5 + y

...and so forth. Do the same thing for the other case. ;)
 

lookagain

Senior Member
Joined
Aug 22, 2010
Messages
2,373
NK8485 & my edit said:
Now I'm on the problem:
ly - 3l = 8 - ly - 3l
Notice that the two expressions inside of the absolute-value bars are the same: y - 3.


\(\displaystyle \ \ \ \ \)|y - 3l = 8 \(\displaystyle \ \) - \(\displaystyle \ \) ly - 3l
+ |y - 3| \(\displaystyle \ \ \ \ \ \ \ \ \) + |y - 3|
---------------------------
\(\displaystyle \ \ \)2|y - 3| = 8


|y - 3| = 4


Now you can finish it and solve it as you did the others.
 
Top