Inequalities with multiplication

Learning Objectives Define an inequality and identify its components. Solve one-step inequalities involving multiplication using inverse operations. Solve one-step inequalities involving division by multiplying both sides. Verify solutions to inequalities by substitution. Explain why multiplying or dividing by a positive number does not change the direction of the inequality sign. Apply inequalities with multiplication to simple real-world scenarios. Have you ever needed to buy more than 5 apples 🍎, but not exactly 5? Or maybe you know you can spend at most $20 on gifts 🎁? These are situations where math inequalities help us! In this lesson, you will learn how to solve mathematical statements called inequalities that involve multiplication. Understanding these will help y...

TermDefinitionExample InequalityA mathematical statement that compares two expressions using symbols like < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).3x < 15 means 'three times a number is less than fifteen'. MultiplicationA mathematical operation that represents repeated addition of the same number. In inequalities, it often appears as a coefficient next to a variable.In 4y ≥ 20, '4y' means 4 multiplied by y. VariableA letter or symbol (like x, y, or a) that represents an unknown number or a quantity that can change.In the inequality 2x < 10, 'x' is the variable. Solution SetThe set of all numbers that make an inequality true. Unlike equations, inequalities often have many solutions.For x < 5, th...

Multiplication Property of Inequality (Positive Number) If $a < b$, then $a \cdot c < b \cdot c$ when $c > 0$. The same applies to >, ≤, and ≥. When you multiply both sides of an inequality by the same positive number, the inequality remains true, and the direction of the inequality sign does not change. This is how you 'undo' division in an inequality. Division Property of Inequality (Positive Number) If $a < b$, then $\frac{a}{c} < \frac{b}{c}$ when $c > 0$. The same applies to >, ≤, and ≥. When you divide both sides of an inequality by the same positive number, the inequality remains true, and the direction of the inequality sign does not change. This is how you 'undo' multiplication in an inequality.