Linear inequalities: word problems

Learning Objectives Translate verbal phrases into mathematical inequalities. Define variables to represent unknown quantities in a real-world scenario. Construct a linear inequality to model a given word problem. Solve multi-step linear inequalities involving one variable. Interpret the solution of a linear inequality in the context of the original problem. Determine if a solution is reasonable and practical for the given scenario. Ever wondered how many items you can put in your online shopping cart without exceeding your budget? 🛒💸 Let's find out! This tutorial will teach you how to translate real-world situations with limits, like budgets or time constraints, into mathematical inequalities. Mastering this skill is essential for making smart, informed decisions in...

TermDefinitionExample InequalityA mathematical statement that compares two expressions using an inequality symbol, showing that one expression is less than, greater than, less than or equal to, or greater than or equal to another.The statement 'x is at least 5' is written as x \geq 5. VariableA symbol, usually a letter like x or y, used to represent an unknown number or a quantity that can change.In the problem 'How many songs can you buy?', 's' could be the variable representing the number of songs. ConstraintA limitation or restriction in a problem that is expressed mathematically, often as an inequality.If you have a $50 gift card, your total spending (c) must be less than or equal to $50. The constraint is c \leq 50. Solution SetThe set of all possible va...

Addition and Subtraction Property of Inequality If a > b, then a + c > b + c and a - c > b - c. You can add or subtract the same number from both sides of an inequality without changing the direction of the inequality symbol. This is used to isolate the variable term. Multiplication and Division Property of Inequality (Positive Number) If a > b and c > 0, then ac > bc and a/c > b/c. You can multiply or divide both sides of an inequality by the same POSITIVE number without changing the direction of the inequality symbol. Multiplication and Division Property of Inequality (Negative Number) If a > b and c < 0, then ac < bc and a/c < b/c. CRITICAL RULE: When you multiply or divide both sides of an inequality by a NEGATIVE number, you MUST...