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

$\sqrt{x^2} = \pm x$ , so the inequality is just $y-x<\pm x$ . 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
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
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1979 AHSME Problems/Problem 13

Problem 13

Solution

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