Question

Absolute Value Inequalities
|x−7|+|1−x|>6

Answer 1

Explanation:

`|x-7|+|1-x|>6\\\\\mathrm{For\:each\:absolute\:find\:positive\:and\:negative\:intervals}\\\\\mathrm{For\:}x\le \:1:\quad x<1\\\\\mathrm{For\:}1<x<7:\quad \mathrm{No\:Solution}\\\\\mathrm{For\:}x\ge \:7:\quad x>7\\\\\mathrm{Combine\:the\:intervals}\\\\<1\quad \mathrm{or}\quad \mathrm{No\:Solution}\quad \mathrm{or}\quad \:x>7\\\\x<1\quad \mathrm{or}\quad \:x>7`