Solve multi-step inequalities

Learning Objectives Define and identify multi-step inequalities. Apply inverse operations to isolate a variable in a multi-step inequality. Correctly reverse the inequality sign when multiplying or dividing by a negative number. Combine like terms and use the distributive property to simplify multi-step inequalities. Solve multi-step inequalities involving variables on both sides. Represent the solution set of a multi-step inequality on a number line. Check the solution to a multi-step inequality. Ever wonder how stores decide how many items they need to sell to make a profit, or how much money you can spend without going over budget? 💰 Inequalities help us answer these kinds of questions! In this lesson, you'll learn how to solve inequalities that require more than...

TermDefinitionExample InequalityA mathematical statement that compares two expressions using an inequality symbol (<, >, ≤, ≥) to show that one is not necessarily equal to the other.$$2x + 5 < 15$$ Multi-Step InequalityAn inequality that requires two or more inverse operations to isolate the variable, often involving combining like terms or using the distributive property.$$3(x - 2) + 7 \ge 16$$ Solution SetThe set of all values for the variable that make the inequality true. Unlike equations, inequalities usually have infinitely many solutions.For $$x > 3$$, the solution set includes 4, 5, 3.1, 100, and any number greater than 3. Inverse OperationsOperations that undo each other (e.g., addition undoes subtraction, multiplication undoes division). We use them to isolate the va...

Addition and Subtraction Properties 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 sign. Multiplication and Division Properties of Inequality (Positive Number) If $$a < b$$ and $$c > 0$$, then $$ac < bc$$ and $$\frac{a}{c} < \frac{b}{c}$$. You can multiply or divide both sides of an inequality by the same positive number without changing the direction of the inequality sign. Multiplication and Division Properties of Inequality (Negative Number) If $$a < b$$ and $$c < 0$$, then $$ac > bc$$ and $$\frac{a}{c} > \frac{b}{c}$$. When you multiply or divide both sides of an inequality by a negat...