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

Aug 8, 2015

{x : x \in \RR, x = –4, 16}

Explanation:

Consider that given every $\left\mid x \right\mid = c$, only two $x$'s fit the bill: $c$ or $- c$. Apply that principle here:

$\left\mid x - 6 \right\mid = 10$
$\setminus R i g h t a r r o w$ $x - 6 = 10$ or x - 6 = –10
$\setminus R i g h t a r r o w$ $x = 16$ or x = –4

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

{x : x \in \RR, x = –4, 16}