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