Question

What is the solution set for |x – 2|– 1 > 2

Answer 1

|x - 2| > 3 <-- I added the one to both sides
x - 2 >3 and x - 2 < -3
x > 5 and x < -1

I hope that makes sense to you!

Answer 2

To find the solution set for absolute value, you make the absolute value stay on one side and put the constant on the other side. Once you have done that, create two new expressions by removing the absolute value bars and have one expression remain the same and for the other expression, flip the symbol and change the sign of the constant.

Answer 3

agentnao has it BUT be careful and write
\[x<-1\text{ OR } x>5\]

Answer 4

not "and" because there is no number that is bigger than 5 AND less than -1. your teacher will be unhappy if you write "and"