Question

What is
`|x-6|` given that
`x \geq 6`

Answer 1

`\mid x-6 \mid \geq 0`

Explanation:

We have two options for x; it is either 6 or greater than 6:

If
`x=6\\`,
`\mid x-6 \mid = \mid 6-6 \mid = \mid 0 \mid = 0\\`.

If
`x > 6`,
`\mid x-6 \mid > \mid 6-6 \mid` =>
`\mid x-6 \mid > 0`.

(for example, if
`x=7\\`,
`\mid x-6 \mid = \mid 7-6 \mid = \mid 1 \mid = 1 > 0`)

So,
`\mid x-6 \mid = 0` or
`\mid x-6 \mid > 0`;
`\mid x-6 \mid \geq 0`.