Question

What is the solution to | 2x-4| >8?

Answer 1

$| 2x-4| \ \textgreater \ 8 \\ \\ 2x - 4 \ \textgreater \ 8 \ , \ -(2x - 4) \ \textgreater \ 8 \ / \ break \ problem \ into \ 2 \ equations \\ \\ first \ equation \\ \\ 2x \ \textgreater \ 8 + 4 \ / \ add \ 4 \ to \ each \ side \\ \\ 2x \ \textgreater \ 12 \ / \ simplify \\ \\ x \ \textgreater \ \frac{12}{2} \ / \ divide\ each \ side \ by \ 2 \\ \\ x \ \textgreater \ 6 \ / \ simplify \\ \\ second \ equation \\ \\ -2x + 4 \ \textgreater \ 8 \ / \ simplify \\ \\ -2x \ \textgreater \ 8 - 4 \ / \ subtract \ 4 \ from \ each \ side \\ \\ -2x \ \textgreater \ 4 \ / \ simplify \\ \\ x \ \textless \ \frac{4}{-2} \ / \ divide \ each \ side \ by \ -2$ 
$\\ \\ x \ \textless \ - \frac{4}{2} \ / \ simplify \\ \\ x \ \textless \ - 2 \ / \ simplify \\ \\ collect \ solutions \\ \\ x \ \textgreater \ 6 \ , \ x \ \textless \ -2$

So, your answer to this problem is x > 6 and x < -2.