Question 1143737
If  | x-2 | >0, which of the following cannot be true? 
A)x>2y
B)x<2y
C)x=2y
D)x=17
<pre>
Let's pick some values for x and y for each choice and see
which one cannot be true.

Let's try choice A:
{{{abs(x-2)>0}}}, {{{x>2y}}}

Let's pick x=1 and y=0.4

{{{abs(1-2)>0}}}, {{{1>2(0.4)}}}
{{{abs(-1)>0}}}, {{{1>0.8}}}
{{{1>0}}}, {{{1>0.8}}}

Both those are true, so answer A can be true, so A is not the 
correct choice.

--------------------------------------

So let's try choice B:

{{{abs(x-2)>0}}}, {{{x<2y}}}

Let's pick x=1 and y=1

{{{abs(1-2)>0}}}, {{{1<2(1)}}}
{{{abs(-1)>0}}}, {{{1<2}}}
{{{1>0}}}, {{{1<2}}}

Both those are true, so answer B can be true, so B is not the 
correct choice.

--------------------------------------

So let's try choice C:

{{{abs(x-2)>0}}}, {{{x=2y}}}

Let's pick x=4 and y=2

{{{abs(4-2)>0}}}, {{{4=2(2)}}}
{{{abs(2)>0}}}, {{{4=4}}}
{{{2>0}}}, {{{4=4}}}

Both those are true, so answer C can be true, so C is not the 
correct choice.

--------------------------------------

So let's try choice D:

{{{abs(x-2)>0}}}, {{{x=17}}}

We must pick x=17

{{{abs(17-2)>0}}}, {{{17=17}}}
{{{abs(15)>0}}}, {{{17=17}}}
{{{15>0}}}, {{{17=17}}}

Both those are true, so answer D can be true, so D is not the 
correct choice.

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So either you copied the problem wrong, or the teacher gave you a 
botched problem.

Edwin</pre>