Graph solutions to one-step inequalities

Learning Objectives Identify the boundary number and inequality symbol in a one-step inequality. Distinguish between open and closed circles when graphing inequalities on a number line. Determine the correct direction to shade on a number line for various inequality symbols. Solve one-step inequalities to isolate the variable. Accurately graph the solution set of a one-step inequality on a number line. Interpret a given graph of an inequality and write its corresponding algebraic expression. Have you ever seen a sign that says 'Speed Limit 65' or 'Must be 48 inches or taller to ride'? 🎢 These are examples of inequalities in the real world! In this lesson, you'll learn how to visually represent the solutions to one-step inequalities on a number line...

TermDefinitionExample InequalityA mathematical statement that compares two expressions using an inequality symbol: < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).x + 3 < 10 Solution to an InequalityAny value(s) for the variable that make the inequality a true statement. Unlike equations, inequalities usually have an infinite number of solutions.For x > 5, numbers like 6, 7.5, and 100 are all solutions. Number LineA visual representation of numbers in order, extending infinitely in both positive and negative directions, used to graph solutions to inequalities.A straight line with evenly spaced tick marks representing integers. Open CircleA hollow circle (o) placed on a number line to indicate that the boundary number is NOT included...

Choosing the Correct Circle for Graphing Use an open circle (o) for strict inequalities: $x < a$ or $x > a$. Use a closed circle (•) for inclusive inequalities: $x \le a$ or $x \ge a$. The type of circle at the boundary number indicates whether that number itself is part of the solution set. 'Equal to' means the point is included (closed circle). Determining Shading Direction After isolating the variable on the left side (e.g., $x < a$): If the inequality symbol is $<$ or $\le$, shade to the left. If the inequality symbol is $>$ or $\ge$, shade to the right. The shading on the number line represents all the numbers that satisfy the inequality. Think of the inequality symbol as an arrow pointing to the solutions when the variable is on the left. S...