Example

Solve for $x: \quad \displaystyle 5=\frac{3x+3}{4}+\frac{5x-1}{7}$

Solution

Let's clear fractions as a first step. The least common multiple of all denominators is $28$ so we multiply both sides by $28$:

or

or

After combining like terms, we get

Now subtract $17$ from both sides to get

Finally we divide both sides by $41$:

or

The equation has the single solution $x=3$.