Problem Solving

Hi folks,

this ques is from OG 12th edition, Q# 130.
I cannot draw line here but it has a number line highlighted from -5 to +3 and ques is: which of the following is an algebraic equation of that:

I chose answer B) |x| <=5
answer that OG gave, E) |x+1| <=4

my reasoning is --> x ranges from -5 to +3, that means, mode of x would always be <=5 , for example if it take -5 then mode is = 5, if it takes +3, mode is <5

what am i missing?

The question wants you to find the equation that fits the line exactly.
Answer (b) doesn't fit it exactly, because I can find an x value that doesn't fall on the highlighted number line.

For example, x = 4.
|4| <= 5 but 4 is not between -5 and +3.

Answer (e) is correct.
|x+1| <= 4
--> x+1 <= 4 and x+1 >= -4
--> x <= 3 and x >= -5