1978 AHSME Problems/Problem 9
Revision as of 01:05, 13 February 2021 by Justinlee2017 (talk | contribs) (Created page with "We have <math>\sqrt{x^2} = |x|</math>, so we rewrite the expression as follows. <cmath>|x - \sqrt{(x-1)^2}| = |x - |x-1||</cmath> We know that <math>x < 0</math>, so <math>x-1...")
We have 
, so we rewrite the expression as follows.
![\[|x - \sqrt{(x-1)^2}| = |x - |x-1||\]](http://latex.artofproblemsolving.com/8/e/7/8e7e72c2db6d3f885a013df9600391c5dc7caf25.png)
We know that 
, so 
. Thus, we can rewrite 
as 
. So
![\[|x - |x-1|| = |x - (1-x)| = |2x - 1|\]](http://latex.artofproblemsolving.com/9/9/9/999a9fe862cdaebfcc24afb50a94f7939aaee628.png)
.
Since 
. Thus, we can write this as
![\[|2x - 1| = 1- 2x\]](http://latex.artofproblemsolving.com/1/f/3/1f396534d8475085751482a5528df752e5be0af0.png)
~JustinLee2017
