Question

What is the solution set for `abs(x – 6) = 10`?

Answer 1

`{x : x \in \RR, x = –4, 16}`

Explanation:

Consider that given every `abs(x) = c`, only two `x`'s fit the bill: `c` or `-c`. Apply that principle here:

`abs(x - 6) = 10`
`\Rightarrow` `x - 6 = 10` or `x - 6 = –10`
`\Rightarrow` `x = 16` or `x = –4`

To express answer in set notation, we use curly brackets and set-builder notation:

`{x : x \in \RR, x = –4, 16}`