For one-step equations, it is generally easy to decide which property of equality will help you find a solution. Most equations are more complex, however. They involve more than one step and may require you to apply the properties of equality, other algebraic properties, and rules about combining like terms.

The table below provides an example of a more complex equation. Click each step to see how you would use multiple rules and properties to solve the equation:

\(\mathsf{ 8x + 12(160 − x + 100) = 48x }\)

Step 1: Clear grouping symbols.	\(\mathsf{ \eqalign{ 8x + 12(160 − x + 100) =& 48x \cr 8x + 1920 − 12x + 1200) =& 48x } }\)
Step 2: Combine like terms.	\(\mathsf{ \eqalign{ 8x + 1920 − 12x + 1200 =& 48x \cr -4x + 3120 =& 48x } }\)
Step 3: Use properties of equality to isolate the variable.	\(\mathsf{ \eqalign{ -4x + 3120 =& 48x \cr -4x + 3120 + 4x =& 48x + 4x \cr 31200 =& 52x \cr \frac{3120}{52} =& \frac{52x}{52} \cr 60 =& x } }\)

Notice how in this solution, the variable ends up on the right side of the equation. That’s fine, though, since you can flip the equation around and not change the outcome.

You try!

The activity below will let you practice solving equations like the ones you’ve seen so far in this lesson. Solve each equation on your own, and then click the Answer button to check your answers.