Question

the inequality 1/2x+3<2x-6 is equivalent to) A. x<-5/6 B. x<6 C. x>-5/6 D. x>6 explain and show work please ​

Answer 1

D. x > 6

Explanation:

`(1)/(2)x+3<2x-6\qquad\text{multiply both sides by 2}\\\\2\!\!\!\!\diagup^1\cdot(1)/(2\!\!\!\!\diagup_1)x+2\cdot3<2\cdot2x-2\cdot6\\\\x+6<4x-12\qquad\text{subtract 6 from both sides}\\\\x<4x-18\qquad\text{subtract 4x from both sides}\\\\-3x<-18\qquad\text{change the signs}\\\\3x>18\qquad\text{divide both sides by 3}\\\\x>6`