Graph solutions to multi-step inequalities

Learning Objectives Solve multi-step inequalities using inverse operations. Correctly apply the rule for reversing the inequality sign when multiplying or dividing by a negative number. Represent the solution set of an inequality on a number line using appropriate open or closed circles. Accurately shade the correct direction on a number line to represent the solution set. Identify and correct common errors made when solving and graphing multi-step inequalities. Interpret the meaning of an inequality's solution set in context. Ever wonder how stores decide what price to put on a sale item, or how much you can spend without going over budget? 💰 Inequalities help us answer these 'at most' or 'at least' questions! In this lesson, you'll learn how...

TermDefinitionExample InequalityA mathematical statement that compares two expressions using an inequality symbol (<, >, ≤, ≥, ≠).2x + 3 > 7 Multi-step InequalityAn inequality that requires two or more inverse operations to isolate the variable.5x - 8 ≤ 12 or 3(x + 1) > 9 Solution SetThe set of all numbers that make an inequality true. Unlike equations, inequalities often have infinitely many solutions.For x > 3, the solution set includes all numbers greater than 3 (e.g., 3.1, 4, 100). Number LineA visual representation of numbers in order, used to graph the solution set of an inequality.A line with evenly spaced tick marks representing integers, with arrows on both ends. Open CircleA hollow circle on a number line used to indicate that the endpoint is NOT included in the s...

Inverse Operations for Inequalities To solve an inequality, apply inverse operations to both sides to isolate the variable, just like with equations. If $a < b$, then: $a + c < b + c$ $a - c < b - c$ Addition and subtraction maintain the direction of the inequality. Use these to move constant terms or variable terms to one side. Multiplication/Division by a Positive Number If $a < b$, and $c > 0$ (c is positive), then: $a \cdot c < b \cdot c$ $\frac{a}{c} < \frac{b}{c}$ Multiplying or dividing both sides of an inequality by a positive number does NOT change the direction of the inequality sign. Multiplication/Division by a Negative Number If $a < b$, and $c < 0$ (c is negative), then: $a \cdot c > b \cdot c$ $\frac{a}{c} > \frac{b}{c}...