## 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.

**Addition, Subtraction, and Division Properties of Equality**- For any numbers a, b, and c,
if \(a=b\), then \(a+c=b+c\). Addition Property of Equality

- if \(a=b\), then \(a-c=b-c\). Subtraction Property of Equality
- if \(a=b\), then \(\frac{a}{c}=\frac{b}{c}\), \(c\ne 0\). Division Property of Equality

- For any numbers a, b, and c,
**The Multiplication Property of Equality**- For any numbers \(ab\) and \(c,a=b\), then \(ac=bc\).
- If you multiply both sides of an equation by the same quantity, you still have equality.