|y|>3 [ ]----][6.) |-3y|<18 [ ][-----][10.)|x-1|<4 [-----][[14.) |x+5/ 3| <2?

Question

solve each absolute-value inequality ? please help me out seriously

Answer 1

I will do two as examples of how this is done.

|y| > 3
y > 3 or -y > 3
y > 3 or y < -3

|x - 1| < 4
x - 1 < 4 and -(x - 1) < 4
x < 5 and x - 1 > -4
x < 5 and x > -3

So for absolute value inequalities, you need to split it into two problems. In one, you deal with the expression inside the absolute value signs, and in the other you deal with its opposite. But if the absolute value is supposed to be less than a positive number, you need to use AND, while if it's supposed to be greater, you need to use OR.