Question

How do you do this question?

Answer 1

x={1,2,3}

Explanation:

The given inequality is

`1 \leqslant (6x - 1)/(3) \: < \: 7`

We multiply through by the LCM of 3 to get:

`3\leqslant 6x - 1\: < \: 21`

We add 1 to both sides to get:

`3 + 1\leqslant 6x \: < \: 21 + 1`

`4\leqslant 6x \: < \: 22`

Divide through by 6 to get:

`(4)/(6) \leqslant x \: < \: (22)/(6)`

This gives us:

`(2)/(3) \leqslant x \: < \: (11)/(3)`

`0.67 \leqslant x \: < \:3.67`

Since x is an integer, the possible values are:

x={1,2,3}