Question

The inequality 6 - 2/3x < x-9 is equivalent to what?

Answer 1

`\large\boxed{x>9}`

Explanation:

`6-(2)/(3)x<x-9\qquad\text{multiply both sides by 3}\\\\3\cdot6-3\!\!\!\!\diagup^1\cdot(2)/(3\!\!\!\!\diagup_1)x<3x-3\cdot9\\\\18-2x<3x-27\qquad\text{subtract 18 from both sides}\\\\-2x<3x-45\qquad\text{subtract 3x from both sides}\\\\-5x<-45\qquad\text{change the signs}\\\\5x>45\qquad\text{divide both sides by 5}\\\\x>9`