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Difference between revisions of "1978 AHSME Problems/Problem 9"

(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...")
(No difference)

Revision as of 02:05, 13 February 2021

We have $\sqrt{x^2} = |x|$, so we rewrite the expression as follows. \[|x - \sqrt{(x-1)^2}| = |x - |x-1||\] We know that $x < 0$, so $x-1 < 0$. Thus, we can rewrite $|x-1|$ as $1-x$. So \[|x - |x-1|| = |x - (1-x)| = |2x - 1|\]. Since $x< 0, 2x-1 < 0$. Thus, we can write this as \[|2x - 1| = 1- 2x\] $\boxed{B}$


~JustinLee2017

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