Lesson 3: Solving Equations with Variables on Both Sides

Property

Step 1. Simplify each side of the equation as much as possible.

• Use the Distributive Property to remove any parentheses.
• Combine like terms.

Step 2. Collect all the variable terms on one side of the equation.

• Use the Addition or Subtraction Property of Equality.

Step 3. Collect all the constant terms on the other side of the equation.

• Use the Addition or Subtraction Property of Equality.

Step 4. Make the coefficient of the variable term to equal to 1.

• Use the Multiplication or Division Property of Equality.
• State the solution to the equation.

Step 5. Check the solution.

• Substitute the solution into the original equation to make sure the result is a true statement.

Examples

Property

If solving an equation with variables on both sides results in a false statement, such as $0 = -10$ or $3 = 7$, then the equation has no solution.

Examples

Property

An equation has infinitely many solutions when algebraic manipulation results in a true statement where both sides are identical, such as $a = a$ where $a$ is any real number.

Examples