Hello!

I'm trying to solve these two questions--
|x-4|<3
and
|5x-2|>5
and I'm not exactly sure how to answer
For question 1 I got this- 1<x<7
and for question 2 I got this-
x>(7)/(5) or x<-(3)/(5)
I'd love some clarification! Thank you so so much!

2 answers

| x - 4 | < 3
rule -> |x| < a -> x < a, x > -a

x - 4 < 3 and x - 4 > -3

solve x - 4 < 3 -> x < 7
solve x - 4 > - 3 -> x > 1
you have x < 7 and x > 1
combine, 1 < x < 7

#2
remember rule ^^
|5x - 2| > 5
remember the "greater" sign calls for "or" at answer

use the rule for absolute value
5x - 2 > 5 OR 5x - 2 < -5

just solve and you'll get

x > 7/5 , x < -3/5
then using the 'or' you have answer
x < -3/5 or x > 7/5
Thank you so much!