To solve linear equations that have mixed numbers, I like to follow a simple method:

1. Change Mixed Numbers: First, turn mixed numbers into improper fractions. For example, $2 \frac{1}{2}$ changes to $\frac{5}{2}$.

2. Remove Fractions: Find the least common denominator (LCD) and multiply the whole equation by it. This helps get rid of the fractions.

3. Group Similar Terms: Put together similar terms on both sides of the equation to make it easier to work with.

4. Get the Variable Alone: Move all the terms with the variable to one side and the numbers without variables to the other side.

5. Solve and Simplify: Lastly, figure out the variable and simplify if you can.

These steps can make solving equations a lot easier and less confusing!