1978 AHSME Problems/Problem 9

Problem 9

If $x<0$ , then $\left|x-\sqrt{(x-1)^2}\right|$ equals

$\textbf{(A) }1\qquad \textbf{(B) }1-2x\qquad \textbf{(C) }-2x-1\qquad \textbf{(D) }1+2x\qquad \textbf{(E) }2x-1$

Solution

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

1978 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
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1978 AHSME Problems/Problem 9

Problem 9

Solution

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