Answer:
x < 2/15
Step-by-step explanation:
[tex]-\dfrac{1}{2}x+\dfrac{2}{3} > \dfrac{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\\\\-\dfrac{1}{2}x+\dfrac{2}{3} > \dfrac{3}{5}\qquad\text{multiply both sides by 30}[/tex]
[tex]30\!\!\!\!\!\diagup^{15}\left(-\dfrac{1}{\not2_1}x\right)+30\!\!\!\!\!\diagup^{10}\dfrac{2}{\not3_1} > 30\!\!\!\!\!\diagup^6 \dfrac{3}{\not5_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<\dfrac{2}{15}}[/tex]
