abs(x) = absolute value of x
A number line with the values -5 to 3 highlighted (inclusive)
Which of the following inequalities is an algebraic expression for the shaded part of the number line above?
(A) abs(x) <= 3
(B) abs(x) <= 5
(C) abs(x-2) <= 3
(D) abs(x-1) <= 4
(E) abs(x+1) <= 4
I (kind of) intuitively understand why that's the answer, but if I do it following the rules of inequalities I get B (in hindsight I can also see why that's wrong). HOW do I solve these without wasting too much time then?