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].

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].

STOP!