Graph solutions to two-step inequalities

Learning Objectives Define and identify two-step inequalities. Solve two-step inequalities using inverse operations. Correctly apply the rules for multiplying or dividing inequalities by negative numbers. Represent the solution set of a two-step inequality on a number line. Distinguish between open and closed circles when graphing inequality solutions. Interpret the meaning of a graphed inequality solution in a real-world context. Ever wonder how stores decide what's a 'good deal' or how much you can spend without going over budget? 💰 Inequalities help us figure out limits and ranges! In this lesson, you'll learn how to solve inequalities that require two steps, just like solving two-step equations. More importantly, you'll discover how to visually...

TermDefinitionExample InequalityA mathematical statement that compares two expressions using an inequality symbol (<, >, ≤, ≥, ≠) to show that one is not necessarily equal to the other.$2x + 5 < 15$ Two-Step InequalityAn inequality that requires two inverse operations to isolate the variable, similar to a two-step equation.$3y - 7 \ge 8$ 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 tick marks representing integers, where solutions are shaded. Open CircleA hollow circle on a number line used...

Properties of Inequality (Addition/Subtraction) If $a < b$, then $a + c < b + c$ and $a - c < b - c$. The same applies to >, ≤, and ≥. You can add or subtract the same number from both sides of an inequality without changing the direction of the inequality symbol. This is the first step in solving many two-step inequalities. Properties of Inequality (Multiplication/Division by a Positive Number) If $a < b$ and $c > 0$, then $ac < bc$ and $\frac{a}{c} < \frac{b}{c}$. The same applies to >, ≤, and ≥. You can multiply or divide both sides of an inequality by the same POSITIVE number without changing the direction of the inequality symbol. Properties of Inequality (Multiplication/Division by a Negative Number) If $a < b$ and $c < 0$, then $...