Question

How do you solve `\frac { x } { 3} \geq 1+ \frac { x } { 6}`?

Answer 1

`x-6>=0`

Explanation:

The first step is to put everything that `x` multiplies in the same side of the equation:
`x/3 >= 1 + x/6` becomes `x/3 - x/6 >= 1`.

Then, you make everything have the same denominator:
`x/3 - x/6 >= 1` becomes `(2x)/6 - x/6 >= 1`.

`(2x)/6 - x/6` can be expressed as `(2x - x)/6`, so:

`(2x - x)/6 >= 1`. We know that `2x - x = x`, so:
`x/6 >= 1`. Making everything have the same denominator, we have:
`x >= 6`, and so `x-6>=0`