Question

What is the solution set for `abs(3x – 24) ≤ 27`?

Answer 1

`-1 <= x <= 17`

Explanation:

Part 1
If `(3x-24) < 0`
then `abs(3x-24) <= 27`
`rArr` `color(white)("XXXX")` `24-3x <= 27`

Adding `3x` to both sides
`color(white)("XXXX")` `color(white)("XXXX")` `24 <= 27 +3x`

Subtracting `27` from both sides
`color(white)("XXXX")` `color(white)("XXXX")` `-3 <= 3x`

Dividing by `3`
`color(white)("XXXX")` `color(white)("XXXX")` `-1 <= x`

Part 2
If `(3x-24) >= 0`
then `abs(3x-24) <= 27`
`rArr` `color(white)("XXXX")` `3x-24 <= 27`

Adding `24` to both sides
`color(white)("XXXXXXXX")` `3x <= 51`

Dividing by `3`
`color(white)("XXXXXXXX")` `x <= 17`

Combining Part 1 and Part 2
`color(white)("XXXX")` `-1 <= x <= 17`