Question

Solve: |x| < 2


A. x < 2
B. -2 < x < 2
C. x > -2
D. x < 0

Answer 1

A. x<2

Answer 2

|x|: -x; x less than 0
x; x greater than 0

So, we have two value and as a result 2 inequalities:
-x<2 and x<2

we need to solve for x in the first inequality ( -x<2).

multiply both sides by -1:
(-1)*-x < 2*(-1)
first we do the multiplication process:
x<-2
finally, change the comparison operator, in this case "<" will become ">" :
x>-2 and this is the same as -2<x

So, we have first inequality (-2<x) and we have the second one (x<2).

-2<x and x<2
It's now time to combine them.

-2<x<2

The answer is letter B.

Forgive me. English is not my first language.