SOLUTION: Solve each inequality. Graph each solution set. The absolute value of x is greater than x-1. I can see that the answer is all reals (by plugging in various numbers from eithe

Question 204172: Solve each inequality. Graph each solution set.
The absolute value of x is greater than x-1.
I can see that the answer is all reals (by plugging in various numbers from either end of the number line), but how is the equation solved mathmatically?
Thank you,
Stella M. Hoy
P.S. This question comes from a worksheet. Glencoe/McGraw-Hill Student Edition Pages 49-54 Practice 1-7 T7 question #10 (Summer Work).
Answer by stanbon(48551) (Show Source):
You can put this solution on YOUR website!
The absolute value of x is greater than x-1.
---------------------------------------
|x| > x-1
-----
Solve the EQUALITY:
|x| = x-1
---
x = x-1
0 = -1
----------------------------
This tells you there are no solutions for the EQUALITY:
-----------------------------------
Check any value of x in the inequality:
x = 1/2
|1/2| > (1/2)- s
1/2 > (1/2)-1
No matter what value you pick for "x", x-1 will be less than |x|
----------------------------------------------------------------------
Graphing you see the solution:

------------------------------------
Solution: All Real Numbers
------------------------------------
Cheers,
Stan H.