**Solve linear equations using the addition and multiplication**

** **

**properties of equality. **Two important properties that are used

in producing equivalent equations are the **addition property of equality**

and the **multiplication property of equality.**

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** **

**Addition and Multiplication Properties of Equality**

** **

**Addition Property of Equality**

For all real numbers *A*, *B*, and *C*, the equations

** A **=

**and**

*B***+**

*A***=**

*C***+**

*B*

*C*are equivalent.

In words, the same number may be added to each side of an equation

without changing the solution set.

**Multiplication Property of Equality**

For all real numbers *A *and *B*, and for *C *≠ 0, the equations

** A **=

**and**

*B***=**

*AC*

*BC*are equivalent.

In words, each side of an equation may be multiplied by the same

nonzero number without changing the solution set.