Question

Suppose the distance between x and zero is less than 1. Write an inequality, not involving absolute values, that describes this situation.

Answer 1

since it says right an inequality, you will have to use <, >, ≥, or ≤

Answer 2

oh it's -1<x<1

Answer 3

no it says the difference of x and 0 so u have to put x - 0 < 1

Answer 4

idk the computer says my answer's correct

Answer 5

fyi: (x - 0) < 1 can be simplified to x<1
but you also want -1 < x (because distance does not care about "direction" i.e. toward -1)
so lawls has the correct answer
x> -1 and x < 1
which can be written -1 < x < 1
in "short-hand"

Answer 6

if you use absolute values you would write
\[ | x - 0 | < 1 \] which simplifies to \[|x|<1 \]