Question

Solve the following inequality. |3n-2|-2<1

Answer 1

`|3n-2|-2<1\\\\|3n-2|<3\\\\3n-2<3 \wedge 3n-2>-3\\\\3n<5 \wedge 3n>-1\\\\n<(5)/(3) \wedge n>-(1)/(3)\\\\n\in \left(-(1)/(3),(5)/(3)\right)`

Answer 2

Answer:
`(-1)/(3)` < n <
`(5)/(3)`

Explanation:

| 3n - 2 | - 2 < 1

+2 +2

| 3n - 2 | < 3

3n - 2 < 3 and 3n - 2 > -3

+2 +2 +2 +2

3n < 5 and 3n > -1

n <
`(5)/(3)` and n >
`(-1)/(3)`

`(-1)/(3)` < n <
`(5)/(3)`

Interval Notation:
`((-1)/(3),`
`(5)/(3))`

Graph:
`(-1)/(3)` o--------------------o
`(5)/(3)`