Example

Solve for $y: \quad \displaystyle -\frac{1}{8}y-\frac{5}{4}=-\frac{1}{3}$

Solution

Let's clear fractions as a first step. The least common multiple of all denominators ($8$, $4$, and $3$) is $24$, so we multiply both sides by $24$:

or

Next, let's add $30$ to both sides to get

Finally we divide both sides by $-3$:

The equation has the single solution $y=-22/3$.