Solve two-step linear inequalities

Learning Objectives Isolate a variable in a two-step linear inequality using inverse operations. Correctly apply the inequality sign reversal rule when multiplying or dividing by a negative number. Represent the solution set of a two-step linear inequality on a number line. Express the solution set of a two-step linear inequality using interval notation. Verify the solution to a two-step linear inequality by substituting a test value. Translate a real-world scenario into a two-step linear inequality and solve it. Ever wondered how to figure out the minimum score you need on a final exam to pass a class? 🤔 Let's find out! This tutorial will guide you through solving two-step linear inequalities, a crucial skill for determining a range of possible solutions rather than...

TermDefinitionExample Linear InequalityA mathematical statement that compares two expressions using an inequality symbol (<, >, ≤, ≥), where the variable has an exponent of 1.3x + 5 > 11 Solution SetThe set of all numbers that make the inequality true.For x > 2, the solution set includes all numbers greater than 2, such as 2.1, 3, and 100. Inverse OperationsOperations that undo each other, used to isolate a variable.Addition and subtraction are inverse operations; multiplication and division are inverse operations. Inequality SymbolsSymbols used to show the relationship between two values.< (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to). Interval NotationA way of writing the solution set of an inequality using parentheses and/or br...

Addition/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. Multiplication/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/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 reverse the direction of the inequality symbol.