Solve this inequality with absolute zero!

| 8/9x - 3 | ≤ 5

what is the solution set?

I got [-18/8 , 9] but it is wrong.

Maybe you need to reduce -18/8.
Your reduced answer would be: [-9/4,9]

|(8/9)x - 3| ≤ 5.
There are two cases to consider: (8/9)x - 3 ≤ 5, and -((8/9)x - 3) ≤ 5 (which is -(8/9)x + 3 ≤ 5).

case 1:
(8/9)x - 3 ≤ 5, or
(8/9)x ≤ 8, or
x ≤ 9.

case 2:
-(8/9)x + 3 ≤ 5, or
-(8/9)x ≤ 2, or
(8/9)x ≥ -2, or
x ≥ -18/8, or
x ≥ -9/4.

The solution, in interval notation, is then [-9/4,9].

edited to correct it, and to say: I didn't use the wrong side; but I did mis-multiply. Oops!

When you solve inequalities you have to do two seperate ways...
First you are going to solve it as a positive. So 9 Is right. Then you have to make the numbers in the absolute vale multiplied by negatives. so it is -8/9x +3 < 5. subtract three from both sides = -8/9x < 2. then when you divide by negative numbers you must switch the sign. so x > -9/4 thatll be answer number two.

| 8/9x - 3 | ≤ 5
-5 <= 8/9x - 3 ≤ 5
-45 <= 8x - 27 ≤ 45
-18 <= 8x ≤ 72
-18/8 <= x ≤ 9

Simplify:
[-9/4, 9]

Answer keys are not infallible. My math book's is full of holes.

| ( 8 / 9 ) * x - 3 | <= 5

( 8 / 9 ) * x - 3 <= 5
( 8 / 9 ) * x <= 5 + 3
( 8 / 9 ) * x <= 8
( 1 / 9 ) * x <= ( 8 / 8 )
x / 9 <= 1
x <= 9 . This is one solution

- [ ( 8 / 9 ) * x - 3 ] <= 5
- ( 8 / 9 ) * x + 3 <= 5
- ( 8 / 9 ) * x <= 5 - 3
- ( 8 / 9 ) * x <= 2
- x / 9 <= ( 2 / 8 )
- x / 9 <= ( 1 / 4 )
-x <= - ( 9 / 4 )

x should be in the range [ - 9 /4 , 9 ]

I agree with the second answer above.