D looks tempting but I will choose E.
Add 2 to each side of the inequality
Therefore non of the available answers will fit with this inequality.
Correct me if I am mistaken.
adding numbers doesn't change the inequality. the inequality remains the same. you said that x+2<6 ==> x<4 ----so we're back to square one.
you have to do it this way.
To check for B.
if x>1 , |x-1| = x-1 then inequality is x-1<3 or x<4
x>1 and x<4 are consistent
if x<1, |x-1| = -(x-1) then inequality is -(x-1)<3 or x>-2
x>-2 and x<1 is again consistent.
Therefore B is correct.
If you try with other answers, you will land up with inconsistent inequalities.
I don't know if there is a shorter method.
Does anyone know a shorter(and quicker) method ?
I'm crossing the bridge.........