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Key Concepts

• Determine whether a number is a solution to an equation.
  1. Substitute the number for the variable in the equation.
  2. Simplify the expressions on both sides of the equation.
  3. Determine whether the resulting equation is true. If it is true, the number is a solution.

  If it is not true, the number is not a solution.

• Subtraction Property of Equality
  • For any numbers [latex]a[/latex] , [latex]b[/latex] , and [latex]c[/latex] ,
    

    if	[latex]a=b[/latex]
    then	[latex]a-b=b-c[/latex]

• Solve an equation using the Subtraction Property of Equality.
  1. Use the Subtraction Property of Equality to isolate the variable.
  2. Simplify the expressions on both sides of the equation.
  3. Check the solution.
• Addition Property of Equality
  • For any numbers [latex]a[/latex] , [latex]b[/latex] , and [latex]c[/latex] ,
    

    if	[latex]a=b[/latex]
    then	[latex]a+b=b+c[/latex]

• Solve an equation using the Addition Property of Equality.
  1. Use the Addition Property of Equality to isolate the variable.
  2. Simplify the expressions on both sides of the equation.
  3. Check the solution.

Glossary

solution of an equation

A solution to an equation is a value of a variable that makes a true statement when substituted into the equation. The process of finding the solution to an equation is called solving the equation.