Question

What are the solutions to the equation |x-10|-4=2x?

Answer 1

`|x-10|=\left\{\begin{array}{ccc}x-10&for&x\geq10\\-(x-10)&for&x < 10\end{array}\right\\.\\\\(1)\qquad x < 10\to|x-10|=-(x-10)=10-x\\\\10-x-4=2x\\6-x=2x\ \ \ |+x\\6=3x\ \ \ \ |:3\\x=2 < 10\\\\(2)\qquad x\geq10\to|x-10|=x-10\\\\x-10-4=2x\\x-14=2x\ \ \ |-x\\x=-14\ \\ot\geq10\\\\Answer:\ x=2`