Multi-step inequalities

Learning Objectives Solve two-step inequalities using inverse operations. Solve multi-step inequalities that require using the distributive property. Solve multi-step inequalities with variables on both sides of the inequality symbol. Correctly apply the rule for reversing the inequality symbol when multiplying or dividing by a negative number. Graph the solution set of a multi-step inequality on a number line. Translate a real-world scenario into a multi-step inequality and find the solution. Ever wonder how many hours you need to babysit to save up *at least* enough money for that new phone? 🤔 Let's find out how math can help! This tutorial will teach you how to solve inequalities that take more than one step. You'll use the skills you already have for solving...

TermDefinitionExample InequalityA mathematical sentence that compares two expressions using symbols like < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).3x + 5 > 11 Solution SetAll the numbers that make an inequality true. Unlike an equation which often has one solution, an inequality has infinitely many solutions.For x > 2, the solution set includes 3, 4.5, 100, and all other numbers greater than 2. Inverse OperationsOperations that 'undo' each other. We use them to isolate the variable, just like in equations.Addition and subtraction are inverse operations. Multiplication and division are inverse operations. Like TermsTerms that have the same variable raised to the same power. You can add or subtract like terms to simplif...

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 on both sides of an inequality without changing the direction of the inequality symbol. Multiplication and Division Property (Positive Number) If a > b and c > 0, then a*c > b*c and a/c > b/c. You can multiply or divide both sides by the same POSITIVE number without changing the direction of the inequality symbol. Multiplication and Division Property (Negative Number) If a > b and c < 0, then a*c < b*c and a/c < b/c. This is the most important rule! If you multiply or divide both sides by a NEGATIVE number, you MUST REVERSE the direction of the inequality symbol.