Problem Solving

og 11#130
Number Line of x:

Number line is from -5 to 5. Numbers -5 <through> 3 are shaded.

Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

(A) |x| <= 3
(B) |x| <= 5
(C) |x - 2| <= 3
(D) |x - 1| <= 4
(E) |x +1| <= 4

<= is "less than or equal to"

If we take values of x=-5 and x=3,we are able to eliminate all options except (b) and (e)
If x=-5,|x|=5 and x=3 satisfies (b).How do u eliminate this option?

we want x to lie between -5 and 3 to correspond with the shaded part

b) |x| <= 5
=>-5<x<5 does not correspond as a part lies outside the shaded region. eliminate

e) |x +1| <= 4
=> -4<x+1<4
=> -4-1<x<4-1
=> -5<x<3 exactly the shaded area.