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 [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.
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CC licensed content, Specific attribution
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