Question

Solve | − 3| < 2. Question 5 options: a) –1 < x < 1 b) –5 < x < –1 c) x d) x

Answer 1

d) 1 < x < 5

Explanation:

`|x-3| < 2` (given)

it does imply two things,

`( x- 3) < 2  ({\textrm}{when} x ≥ 3)` -------(1)

`(3-x)</strong>  <strong>< 2  ({\textrm}{when} x < 3)` --------(2)

from (1),

`x < 5` -----(3)

from (2)

`x >1` -------(4)

so from (3) and (4)

`1 < x < 5` (Answer)