Question

How do i solve this?

Answer 1

`\large\boxed{x<-(8)/(15)}`

Explanation:

`-(1)/(2)x+(1)/(3)>(3)/(5)\\\\\text{Find common denominator of the fractions}\\\\2,\ 3,\ 5\to2\cdot3\cdot5=30\\\\-(1)/(2)x+(1)/(3)>(3)/(5)\qquad\text{multiply both sides by 30}\\\\30\!\!\!\!\!\diagup^(15)\left(-(1)/(2\!\!\!\!\diagup_1)x\right)+30\!\!\!\!\!\diagup^(10)\left((1)/(3\!\!\!\!\diagup_1)\right)>30\!\!\!\!\!\diagup^(6)\left((3)/(5\!\!\!\!\diagup_1)\right)\\\\-15x+10>(6)(3)\\\\-15x+10>18\qquad\text{subtract 10 from both sides}`

`-15x>8\qquad\text{change the signs}\\\\15x<-8\qquad\text{divide both sides by 15}\\\\x<-(8)/(15)`