Mathematics » Introducing Decimals » Solve Equations with Decimals

Key Concepts

This is a lesson from the tutorial, Introducing Decimals and we encourage you to log in or register before you continue, so that you can track your progress.

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Key Concepts

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

      If so, the number is a solution.

       

      If not, the number is not a solution.

  • Properties of Equality
Subtraction Property of EqualityAddition Property of Equality
For any numbers \(a\), \(b\), and \(c\),

 

\(\text{If } a = b\)
\(\text{then } a − c = b − c\)

For any numbers \(a\), \(b\), and \(c\),

 

\(\text{If } a = b\)
\(\text{then } a + c = b + c\)

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

 

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

For any numbers \(a\), \(b\), and \(c\),

 

\(\text{If } a = b\)
\(\text{then } a⋅c = b⋅c\)

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