What Is the Distributive Property?
Before we can solve equations with brackets, we need to understand the distributive property , one of the most useful tools in algebra.
Distributive Property: When a number or term is multiplied by a group of terms inside brackets, it is multiplied by every term inside. In general:
For example:
- ← notice the variable inside can have its own coefficient too!
Imagine you're handing out $5 to each person in a group of people. You give $5 to each of the people and $5 to each of the 4 extra people , that's total. The 5 is "distributed" to everyone in the bracket.
The distributive property lets us expand brackets, turning a product into a sum that's easier to work with when solving equations.
Equations with Brackets , Two Strategies
When you have an equation like , there are two valid approaches:
Strategy 1: Divide first (if the bracket is multiplied by a number)
Divide both sides by the number outside the bracket to remove it, then solve the simpler equation.
Strategy 2: Expand first (distribute, then solve)
Multiply out the bracket first, then collect terms and isolate the variable.
Both strategies give the same answer , choose whichever feels cleaner for the numbers involved.
If the number outside the bracket divides evenly into the number on the other side of the equation, dividing first is usually quicker. If not, expanding first may be easier.
For example, with : since divides cleanly, dividing first is great here.
But with : since 40 is not divisible by 3, expanding first is the better choice:
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