Graph solutions to two-step inequalities

Learning Objectives Solve two-step inequalities using inverse operations. Identify the correct inequality symbol and its meaning. Determine whether to use an open or closed circle when graphing inequality solutions. Graph the solution set of a two-step inequality on a number line. Interpret the meaning of a graphed inequality solution. Check if a given value is a solution to a two-step inequality. Ever wonder how stores decide how many items to stock, or how fast you can drive without getting a ticket? 🚦 These situations often involve limits, which we can describe using inequalities! In this lesson, you'll learn how to solve mathematical statements that show a range of possibilities, not just one exact answer. You'll also discover how to visually represent these...

TermDefinitionExample InequalityA mathematical statement that compares two expressions using symbols like < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).x + 3 > 7 Solution to an InequalityAny value(s) for the variable that makes the inequality true. Unlike equations, inequalities usually have many solutions.For x > 5, values like 6, 7.5, and 100 are all solutions. Two-Step InequalityAn inequality that requires two inverse operations to isolate the variable.2x - 5 < 11 Graphing an InequalityRepresenting the solution set of an inequality on a number line using circles and arrows.A line starting at 3 and going to the right with an open circle at 3 represents x > 3. Open CircleUsed on a number line to show that the endpoint is *no...

Solving Two-Step Inequalities To solve an inequality of the form $ax + b < c$ (or >, ≤, ≥), first add or subtract $b$ from both sides, then multiply or divide by $a$. Use inverse operations in the reverse order of operations (undo addition/subtraction first, then multiplication/division) to isolate the variable. Flipping the Inequality Sign When multiplying or dividing *both sides* of an inequality by a *negative number*, you MUST reverse the direction of the inequality sign. This rule ensures the inequality remains true. For example, if $2 < 5$, then multiplying by -1 gives $-2 > -5$ (the sign flips). Graphing Rules for Inequalities For $<$ or $>$: Use an **open circle** at the endpoint. For $\le$ or $\ge$: Use a **closed circle** at the endpoint. If...