# Summary: Solving Equations Using the Division and Multiplication Properties of Equality

## Key Concepts

**Division and Multiplication Properties of Equality**

**Division Property of Equality:**For all real numbers*a, b, c,*and$c\ne 0$, if$a=b$, then$ac=bc$.**Multiplication Property of Equality:**For all real numbers*a, b, c,*if$a=b$, then$ac=bc$.

**Solve an equation with variables and constants on both sides**

- Choose one side to be the variable side and then the other will be the constant side.
- Collect the variable terms to the variable side, using the Addition or Subtraction Property of Equality.
- Collect the constants to the other side, using the Addition or Subtraction Property of Equality.
- Make the coefficient of the variable$1$, using the Multiplication or Division Property of Equality.
- Check the solution by substituting into the original equation.

**General strategy for solving linear equations**

- Simplify each side of the equation as much as possible. Use the Distributive Property to remove any parentheses. Combine like terms.
- Collect all the variable terms to one side of the equation. Use the Addition or Subtraction Property of Equality.
- Collect all the constant terms to the other side of the equation. Use the Addition or Subtraction Property of Equality.
- Make the coefficient of the variable term equal to $1$. Use the Multiplication or Division Property of Equality. State the solution to the equation.
- Check the solution. Substitute the solution into the original equation to make sure the result is a true statement.