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Help with basic calculus :) - Easy 10 Points.?
|x - 8| = |2-x| - 6
Solve for value(s) of x.
Thanks a lot. Brackets are absolute signs.
yeah, unfortunately x doesn't equal to 2. :)
i think crazychick is getting closer, however the answer is still incorrect :S
oops, crazychild** my bad srry.
4 Answers
- 1 decade agoFavourite answer
Break the range of x up into 3 intervals:
(1) x > 8
(2) 2 <= x <= 8
(3) x < 2
For (1), we have x - 8 = x - 2 - 6 i.e. true for all x > 8
For (2), we have 8 - x = x - 2 - 6 i.e. 2x = 16 i.e. x = 8
For (3), we have 8 - x = 2 - x - 6 i.e. not true for any x < 2
So putting everything together x >= 8
- crazychildLv 51 decade ago
There are numerous scenarios.
1st lets just remove the absolute signs.
x - 8 = 2 - x - 6
2x = 4
x = 2
-(x-8) = 2 - x - 6
-x + 8 = -4 - x
12 = 0, false so no solution here.
x - 8 = -(2-x) - 6
x - 8 = -2 + x - 6
0 = 0, degenerate solution
-(x-8) = -(2-x) - 6
-x + 8 = -2 + x - 6
16 = 2x
x = 8
So there is only 2 solutions: x = 2, 8
Source(s): My brain :-D - 1 decade ago
(x - 8) = (2 - x) -6
x - 8 = 2 - x - 6
x - 8 + 6 = 2 - x
x - 2 = 2 - x
x + x = 2 + 2
2x = 4
x = 4/2
x = 2
there you go. i'm sure you know the rules.
good luck
edit : oh really? well then, I'm not sure. sorry
- 1 decade ago
x-8=2-x-6
x-8=-x-4
2x=4
x=2
Plug 2 in for x in the original equation:
|2-8|=|2-2|-6
|-6|=|0|-6
6=-6
x=2 is NOT a correct solution
-|x-8|=-|2-x|-6
-x+8=-2+x-6
-x+8=x-8
16=2x
x=8
plug 8 in for x in the original equation
|8-8|=|2-8|-6
|0|=|-6|-6
0=6-6
0=0
x=8 is a correct solution
