Addition property

Definition

The addition property states that if you add the same value to both sides of an equation or inequality, the equality or inequality remains true. This property is fundamental for solving equations and inequalities.

5 Must Know Facts For Your Next Test

1. Adding a constant to both sides of an equation does not change its solution.
2. The addition property is valid for both equations and inequalities.
3. When using the addition property in inequalities, ensure you maintain the inequality direction unless multiplying by a negative number.
4. This property helps isolate variables when solving linear equations.
5. In absolute value inequalities, applying the addition property can simplify expressions before splitting into two cases.

Review Questions

• What happens to an equation if you add the same number to both sides?
• How does the addition property apply differently when solving inequalities compared to equations?
• Why is it important to use the addition property when isolating variables in linear equations?

Related terms

Subtraction Property: If you subtract the same value from both sides of an equation or inequality, the equality or inequality remains true.

Multiplication Property: If you multiply both sides of an equation or inequality by the same non-zero value, the equality or inequality remains true.

Division Property: \text{If you divide both sides of an equation or inequality by a non-zero value, the equality or inequality remains true.}