1979 AHSME Problems/Problem 13

Problem 13

The inequality $y-x<\sqrt{x^2}$ is satisfied if and only if

$\textbf{(A) }y<0\text{ or }y<2x\text{ (or both inequalities hold)}\qquad \textbf{(B) }y>0\text{ or }y<2x\text{ (or both inequalities hold)}\qquad \textbf{(C) }y^2<2xy\qquad \textbf{(D) }y<0\qquad \textbf{(E) }x>0\text{ and }y<2x$

Solution

Solution by e_power_pi_times_i

$\sqrt{x^2} = \pmx$ (Error compiling LaTeX. Unknown error_msg), so the inequality is just $y-x<\pmx$ (Error compiling LaTeX. Unknown error_msg). Therefore we get the two inequalities $y<0$ and $y<2x$ . Checking the answer choices, we find that $\boxed{\textbf{(A) } y<0\text{ or }y<2x\text{ (or both inequalities hold)}}$ .

1979 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 12	Followed by Problem 14
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1979 AHSME Problems/Problem 13

Problem 13

Solution

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