Difference between revisions of "2011 AMC 10A Problems/Problem 7"

(Created page with '==Problem 7== Which of the following equations does NOT have a solution? <math>\text{(A)}\:(x+7)^2=0</math> <math>\text{(B)}\:|-3x|+5=0</math> <math>\text{(C)}\:\sqrt{-x}-2=0<…')
 
(Problem 7)
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<math>\text{(E)}\:|-3x|-4=0</math>
 
<math>\text{(E)}\:|-3x|-4=0</math>
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<math>|-3x|+5=0</math> has no solution because absolute values output positives and this equation implies that the absolute value could output a negative.
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Further:
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<math>(x+7)^2 = 0</math> is true for <math>x = -7</math>
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<math>\sqrt{-x}-2=0</math> is true for <math>x = -4</math>
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<math>\sqrt{x}-8=0</math> is true for <math>x = 64</math>
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<math>|-3x|-4=0</math> is true for <math>x = \frac{4}{3}, -\frac{4}{3}</math>

Revision as of 01:51, 11 February 2011

Problem 7

Which of the following equations does NOT have a solution?

$\text{(A)}\:(x+7)^2=0$

$\text{(B)}\:|-3x|+5=0$

$\text{(C)}\:\sqrt{-x}-2=0$

$\text{(D)}\:\sqrt{x}-8=0$

$\text{(E)}\:|-3x|-4=0$


$|-3x|+5=0$ has no solution because absolute values output positives and this equation implies that the absolute value could output a negative.

Further: $(x+7)^2 = 0$ is true for $x = -7$

$\sqrt{-x}-2=0$ is true for $x = -4$

$\sqrt{x}-8=0$ is true for $x = 64$

$|-3x|-4=0$ is true for $x = \frac{4}{3}, -\frac{4}{3}$

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