Question

For what valuels of x is the equation |4x + 2| = x + 8 TRUE?

Answer 1

`x=-2\quad \mathrm{or}\quad \:x=2`

Explanation:

`|4x + 2| = x + 8 \\\\\mathrm{For\:each\:absolute\:find\:positive\:and\:negative\:intervals}\\\\\mathrm{Solve\:the\:inequality\:for\:each\:interval:}\\\\\mathrm{For\:}x<-(1)/(2):\quad x=-2\\\\\mathrm{For\:}x\ge \:-(1)/(2):\quad x=2\\\\\mathrm{Combine\:Solutions:}\\\\x=-2\quad \mathrm{or}\quad \:x=2`