Example

Solve for $x: \quad \displaystyle \frac{9x}{8}-2=\frac{11x}{10}$

Solution

This is another example where it's good to start by clearing fractions. The least common multiple of all denominators ($8$, $1$, and $10$) is $40$, so we multiply both sides by $40$:

or

Next, let's get the $x$'s all on one side by subtracting $44x$ to both sides:

or

The equation has the single solution $x=80$.