Solve the Fraction Equation: Finding X in 8/3 - 4/5x = -2/10x

This equation has multiple terms with different denominators (3, 5, 10). Cross-multiplication only works for simple one fraction equals one fraction problems. The LCD method handles complex equations efficiently.

List multiples of the largest denominator (10): 10, 20, 30, 40... The first number that's divisible by all denominators (3, 5, 10) is your LCD. So $\frac{30}{3} = 10$, $\frac{30}{5} = 6$, $\frac{30}{10} = 3$.

Yes! Notice $-\frac{2}{10}x = -\frac{1}{5}x$. Simplifying first makes the LCD easier to find. Your LCD becomes 15 instead of 30, making calculations simpler.

Any common multiple works, but the LCD gives the simplest numbers. Using 60 instead of 30 gives the same answer but with bigger numbers: $160 - 48x = -12x$ still leads to $x = \frac{40}{9}$.

Many linear equations have fractional solutions! $\frac{40}{9}$ is already in simplest form since 40 and 9 share no common factors. Converting to mixed number: $4\frac{4}{9}$.

Substitute $x = \frac{40}{9}$ into the original equation:

• Left side: $\frac{8}{3} - \frac{4}{5} \cdot \frac{40}{9} = \frac{8}{3} - \frac{32}{9} = \frac{-8}{9}$
• Right side: $-\frac{2}{10} \cdot \frac{40}{9} = -\frac{8}{9}$

Both sides equal $-\frac{8}{9}$, so our answer is correct!