Question

Solve. -1/2x + 2/3 > 3/5

Answer 1

x < 2/15

Explanation:

`-(1)/(2)x+(2)/(3) > (3)/(5)\\\\\text{Find the common denominator.}\\\\\text{Multiples of 2:}\ 0,\ 2,\ 4,\ 6,\ 8,\ 10,\ 12,\ 14,...,\ \boxed{30},\ ...\\\\\text{Multiples of 3:}\ 0,\ 3,\ 6,\ 9,\ 12,\ 15,\ ...,\ \boxed{30},\ ...\\\\\text{Multiples of 5:}\ 0,\ 5,\ 10,\ 15,\ 20,\ 25,\ \boxed{30},\ ...\\\\\text{The common denominator is 30.}\\\\30=2\cdot15\\30=3\cdot10\\30=5\cdot6\\\\-(1)/(2)x+(2)/(3) > (3)/(5)\qquad\text{multiply both sides by 30}`

`30\!\!\!\!\!\diagup^(15)\left(-(1)/(\\ot2_1)x\right)+30\!\!\!\!\!\diagup^(10)(2)/(\\ot3_1) > 30\!\!\!\!\!\diagup^6 (3)/(\\ot5_1)\\\\(15)(-x)+(10)(2)>(6)(3)\\\\-15x+20>18\qquad\text{subtract 20 from both sides}\\\\-15x>-2\qquad\text{change the signs}\\\\15x<2\qquad\text{divide both sides by 15}\\\\\boxed{x<(2)/(15)}`