Multiplication property

Definition

The multiplication property states that you can multiply both sides of an equation or inequality by the same nonzero number without changing the solution set. This property is crucial for solving linear inequalities and absolute value inequalities.

5 Must Know Facts For Your Next Test

1. Multiplying both sides of an inequality by a positive number preserves the direction of the inequality.
2. Multiplying both sides of an inequality by a negative number reverses the direction of the inequality.
3. The multiplication property is used to isolate variables in linear inequalities.
4. When applying this property to absolute value inequalities, remember to consider both possible cases (positive and negative).
5. This property is fundamental for transforming equations and inequalities into simpler forms.

Review Questions

• What happens to the direction of an inequality when you multiply both sides by a negative number?
• How would you use the multiplication property to solve $3x < 9$?
• Why is it important to consider both positive and negative cases when dealing with absolute value inequalities?

Related terms

Linear Inequality:

An inequality involving a linear function, which can be solved using properties like addition, subtraction, multiplication, and division.

Absolute Value Inequality:

An inequality that contains an absolute value expression, requiring consideration of both positive and negative solutions.

Addition Property: A principle stating that adding the same number to both sides of an equation or inequality does not change its solution set.