## Thomas' Calculus 13th Edition

$x\in(-\infty,-0)\cup(2,\infty)$
Use properties from the table 'Absolute Values and Intervals". Applying Property 7: $|x|\gt a\quad\Leftrightarrow\quad x\gt a\ \$or$\ \ x\lt-a, \quad$ for a = positive number We have $\begin{array}{ll} 1-x\gt 1 & /-1\\ -x\gt0 & /\times(-1)\\ x\lt 0 & \end{array}$ $\ \$ or $\ \$ $\begin{array}{ll} 1-x\lt -1 & /-1\\ -x\lt -2 & /\times(-1)\\ x\gt2 & \\ & \end{array}$ In interval form, we can write this result as $x\in(-\infty,-0)\cup(2,\infty)$