im a bit confused this is due soon its precalculus

Question

Solve: 

Give your answer as an interval.

Answer 1

3x-2<9 or 3x-2 >-9

3x<11

3x>-7

x < 11/3

x>-7/3

x is in the interval (-7/3, 11/3) or (-2 1/3, 3 2/3)

Try testing that solution with some simple integers in the interval and outside the interval. x= 0, 1<9, x= 4, 12-1>9, x=-3 10>9.

when x=-7/3 or 11/3, 9=9, so use parentheses, not brackets, for the ends of the interval, as the interval does not include the boundaries.

the absolute value signs mean that either 3x-2 <9 or -(3x-2)<9

3x-2<9

x <11/3 is sort of straight forward,

but the 2nd part a little more complex

-(3x-2)<9

-3x +2 <9

-3x <9-2

-3x<7

here's the tricky part, divide by -3, but when you divide (or multiply by a negative number), the direction of the inequality changes direction, so

x>-7/3

which is the same as

-7/3<x

combine that with what you got from the 1st inequality, x<10/3 to get

-7/3<x<11/3, that's the interval of the solution for x, or write as

(-7/3, 11/3) or (-2 1/3, 3 2/3)