## Key Concepts

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

**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[latex]1[/latex], 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 [latex]1[/latex]. 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.