If x|x|<x which of the following must be true about x?

Question

(A) x>1x>1
(B) x>−1x>−1
(C) |x|<1|x|<1
(D) |x|=1|x|=1
(E) |x|2>1

Answer 1

+X < X/X +X<1 X has to be less than 1

-X < X/X -X<1 X > -1 X has to be greater than -1

-1 < X < 1 creates the boundaries of what X could be that does not violate the question assumptions.

Create a X-Y graph. 2 equations. X=1 and X=-1, ignore the < or >.

Thats 2 vertical lines at X=1 and the other at X=-1

Then apply the < and >. That visually places X in between -1 and +1.

Understanding this, the easiest way to answer the question is to plug in numbers around boundary values, 1 and -1, such as -2,-1,0,1,2. After the condition is violated, the test is designed to fold into one or two violations rather than wasting time for the student to try -10,-5,-3, 3,5,10 or a bunch of other more complex trial and error.