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Key Concepts

• How to determine whether a number is a solution to an equation.
  • Step 1. Substitute the number for the variable in the equation.
  • Step 2. Simplify the expressions on both sides of the equation.
  • Step 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.
• Properties of Equalities
  

  Subtraction Property of Equality	Addition Property of Equality
  For any numbers [latex]a,b,c[/latex], if [latex]a=b[/latex] then [latex]a-c=b-c[/latex].	For any numbers [latex]a,b,c[/latex], if [latex]a=b[/latex] then [latex]a+c=b+c[/latex].

• Division Property of Equality
  • For any numbers [latex]a,b,c[/latex], and [latex]c\ne 0[/latex]

If [latex]a=b[/latex] , then [latex]\Large{\frac{a}{c}=\frac{b}{c}}[/latex].