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

Revision as of 20:34, 10 January 2018

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 $x = \frac{4}{3}, -\frac{4}{3}$

Therefore, the answer is $\boxed{\mathrm{(B)}}$ .

Instead of solving, we can just categorize and solve.

[hide=Section 1] This contains $\mathrm{(A),(C),(D)} [/hide]

2011 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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
All AMC 10 Problems and Solutions

@@ Line 13: / Line 13: @@
-== Solution ==
+== Solution 1 ==
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 Therefore, the answer is <math> \boxed{\mathrm{(B)}} </math>.
+==Solution 2==
+Instead of solving, we can just categorize and solve.
+[hide=Section 1]
+This contains $\mathrm{(A),(C),(D)}
+[/hide]
 == See Also ==
 {{AMC10 box|year=2011|ab=A|num-b=6|num-a=8}}
 {{MAA Notice}}