Solve one-step linear inequalities multiplication and division

Learning Objectives Identify the inverse operation needed to isolate a variable in a one-step inequality. Solve one-step linear inequalities by multiplying or dividing by a positive number. Solve one-step linear inequalities by multiplying or dividing by a negative number. Correctly apply the rule of reversing the inequality symbol when multiplying or dividing by a negative number. State the solution to an inequality in proper notation. Verify the solution set of an inequality by testing a value. You have $50 to spend on snacks for a party, and each snack costs $4. How many snacks can you buy at most? 🤔 Let's use inequalities to find out! This tutorial will teach you how to solve one-step inequalities that involve multiplication and division. Mastering this skill is f...

TermDefinitionExample InequalityA mathematical statement that compares two values or expressions that are not equal, using symbols like < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).The statement `5x \geq 10` is an inequality. Solution SetThe set of all numbers that make an inequality true when substituted for the variable.For the inequality `x > 2`, the solution set includes 3, 4.5, 100, and any other number greater than 2. CoefficientA numerical or constant quantity placed before and multiplying the variable in an algebraic expression.In the term `-7y`, the coefficient is -7. Inverse OperationAn operation that reverses the effect of another operation. Multiplication and division are inverse operations of each other.To undo multiplyi...

Multiplication/Division Property of Inequality (Positive Number) If `a < b` and `c` is a positive number (`c > 0`), then `ac < bc` and `a/c < b/c`. When you multiply or divide both sides of an inequality by a positive number, the inequality symbol remains the same. This rule applies to all inequality symbols (>, <, ≥, ≤). Multiplication/Division Property of Inequality (Negative Number) If `a < b` and `c` is a negative number (`c < 0`), then `ac > bc` and `a/c > b/c`. This is the most critical rule: when you multiply or divide both sides of an inequality by a negative number, you MUST reverse the direction of the inequality symbol. For example, `<` becomes `>` and `≥` becomes `≤`.