Question

What are the integer solutions to the inequality below? 3 ≤ 3 x − 4 ≤ 2 x + 1

Answer 1

`x` can be
`3`,
`4`, or
`5`

Explanation:

Let's split the inequality and solve it piece by piece.

Case:
`3<=3x-4`

We add
`4` to both sides to get
`7<=3x`.

We divide both sides by
`3` to get
`7/3<=x`.

So,
`x>=7/3`.

Case:
`3x-4<=2x+1`

We subtract 2x from both sides to get
`x-4<=1`.

We add
`4` to both sides to get
`x<=5`.

So, we want to find the integer solutions to
`7/3<=x<=5`.

`7/3= 2 1/3`, so
`x` can be
`3`,
`4`, or
`5`.

So,
`x` can be
`3`,
`4`, or
`5` and we're done!