Mathematics » Introducing Integers » Solve Equations Using Integers; The Division Property of Equality

Key Concepts

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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 EqualityAddition Property of Equality
    \(\text{For any numbers}\phantom{\rule{0.2em}{0ex}}a,b,c,\)

     

    \(\text{if}\phantom{\rule{0.2em}{0ex}}a=b\phantom{\rule{0.2em}{0ex}}\text{then}\phantom{\rule{0.2em}{0ex}}a-c=b-c.\)

    \(\text{For any numbers}\phantom{\rule{0.2em}{0ex}}a,b,c,\)

     

    \(\text{if}\phantom{\rule{0.2em}{0ex}}a=b\phantom{\rule{0.2em}{0ex}}\text{then}\phantom{\rule{0.2em}{0ex}}a+c=b+c.\)

  • Division Property of Equality
    • For any numbers \(a,b,c,\) and \(c\ne 0\)
       

      If \(a=b\), then \(\frac{a}{c}=\frac{b}{c}\).

 

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