Question

Can some please help explain to me how they'd split up |3x+2|<4 to find the solution set?

Answer 1

1. to get rid of the absolute value, you have to square both the sides.
OR
2. create two inequalities , one opsitive and one for negative

Answer 2

Use two case
when 3x+2>0
\[3x+2<4\]
3x+2<0
\[-(3x+2)<4\]
Solve both the cases for x, you'll get a range for x, make sure that original condition is satisfied

Answer 3

Suppose you assume x>0
and after solving an inequality you get x<-1
then that case, there would be no answer

Answer 4

Do you get the idea?

Answer 5

Yes, you explain things so perfectly! It makes total sense now :)