Respuesta :

Answer:

d) 1 < x < 5

Step-by-step explanation:

[tex] |x-3| < 2 [/tex] (given)

it does imply two things,

[tex] ( x- 3) < 2  ({\textrm}{when} x ≥ 3) [/tex] -------(1)

[tex] (3-x)  < 2  ({\textrm}{when} x < 3) [/tex] --------(2)

from (1),

[tex] x < 5 [/tex] -----(3)

from (2)

[tex] x >1 [/tex]  -------(4)

so from (3) and (4)

[tex] 1 < x < 5 [/tex] (Answer)