When |x|1 and |x-3|1, which of the following is contained in the sco

Question

When |x|>1 and |x-3|>1, which of the following is contained in the scope of x?

A. -0.5 
B. 0 
C. 0.5 
D. 1.5 
E. 2.5

chetan2u · Accepted Answer

When |x|>1 and |x-3|>1, which of the following is contained in the scope of x? A. -0.5 B. 0 C. 0.5 D. 1.5 E. 2.5 Contained in the scope of x in simple terms means ' Which of the choices fit in the range of x'. Now |x|>1 means x<-1 and x>1 |x-3|>1 means x-3>1.. x>4 or 3-x>1 or x<2 .. Common range is x<-1, 14.. Only 1.5 falls in one of the range above 11 and |x-3|>1 to check what fits in. A. -0.5……|-0.5|>1……NO B. 0 ……|0|>1……NO C. 0.5 ……|0.5|>1……NO D. 1.5 ……|1.5|>1……YES and |1.5-3|>1……YES E. 2.5 ……|2.5|>1……YES and |2.5-3|>1……NO Analyse on a NUMBER line |x|>1 means x has to be more than one away from 0. So discard anything between -1 and 1, both inclusive. A, B and C are gone. |x-3|>1 means x will be more than one away from 3. So cannot be between 2 and 4, both inclusive. E is gone so D

pushpitkc · Answer

Going by the answer options, Only x = 1.5(Option D) is contained in the scope of x

When x=1.5, |x| = 1.5 > 1 and |x-3| = |1.5 - 3| = |-1.5| > 1

tanvi9 · Answer

by simplifying modulus, x has following solutions: X >1 X< -1 X<2 X>4 choice D satisfies 2nd and 3rd solution, so D. try number line and plot if solutions make it messy.

MathRevolution · Answer

==> |x|>1 becomes x<-1 or 11, you get x-3<-1 or 1 x<2 or 4

vamkrispk · Answer

can anyone please explain what scope of x means and how 1.5 was considered.. i am confused

PCSund · Answer

Drawing out on number line makes 1.5 obvious choice

rocky620 · Answer

MathRevolution  Hi,

Doesn't, x<-1 satisfies both conditions?

MathRevolution · Answer

Hello,

That is one of the inequalities that satisfies but doesn't satisfy the range.

Combine all possible conditions to get the range or scope.

Thanks

kkannan2 · Answer

Hi MathRevolution , wouldn't the overlap of the inequalities be x<-1; 14 since these ranges satisfy the cases given? Let me know if I'm missing something here, you had said above that the common range is 14. I'm confused as to why x<-1 was left out, since we get x<-1 from the first inequality and x<2 from the second inequality; x<-1 will satisfy both. I got the correct answer for this question, but was just wondering how to combine inequalities like this for future questions. Thanks, Kaushik

bumpbot · Answer

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When |x|>1 and |x-3|>1, which of the following is contained in the sco

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