Question

7/2x-5/2x=20/3x+10 find the answer

Answer 1

Let $\frac{1}{x}=t$

The equation $\frac{7}{2x}- \frac{5}{2x}= \frac{20}{3x}+10$ becomes $\frac{7}{2}t- \frac{5}{2}t= \frac{20}{3}t+10$

$\frac{7}{2}t- \frac{5}{2}t= \frac{20}{3}t+10\\ \\ \Rightarrow \frac{7}{2}t- \frac{5}{2}t -\frac{20}{3}t=10\\ \\ \Rightarrow \frac{7t \times 3-5t \times 3-20t \times 2}{6} =10\\ \\ \Rightarrow \frac{21t-15t-40t}{6} =10\\ \\ \Rightarrow -34t=10 \times 6=60\\ \\ \Rightarrow t=- \frac{60}{34}=- \frac{30}{17} \\\\ \Rightarrow \frac{1}{x}= - \frac{30}{17} \\\\ \Rightarrow x= - \frac{17}{30}$