Graph inequalities

Learning Objectives Identify the four inequality symbols and their meanings. Translate verbal phrases into algebraic inequalities. Represent the solution set of a single-variable inequality on a number line. Correctly use open and closed circles to indicate whether a boundary point is included in a solution set. Solve and graph multi-step single-variable inequalities. Graph compound inequalities involving 'and' (intersections) and 'or' (unions). Write an algebraic inequality from its graph on a number line. Ever seen a sign that says 'Maximum capacity: 250 people'? How would you show ALL the possible numbers of people allowed? 🧑‍🤝‍🧑 This tutorial will teach you how to visually represent all the possible solutions to an inequality on a numb...

TermDefinitionExample InequalityA mathematical statement that compares two values or expressions that are not equal. It uses one of the following symbols: < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).x + 5 > 12 Solution SetThe set of all numbers that make an inequality true. For single-variable inequalities, this is often an infinite range of numbers.For x > 7, the solution set includes 7.1, 8, 10, 95, and all other numbers greater than 7. Boundary PointThe number that separates the solutions from the non-solutions on a number line. It is the value where the expression is equal to the other side.In the inequality x ≤ -2, the boundary point is -2. Open Circle (Hollow Dot)A symbol used on a number line to indicate that the boundary...

Graphing Strict Inequalities For x > a or x < a, use an open circle at point 'a'. When the inequality symbol is > (greater than) or < (less than), the boundary point 'a' is not a solution. The open circle visually represents this exclusion. Shade to the right for '>' and to the left for '<'. Graphing Inclusive Inequalities For x ≥ a or x ≤ a, use a closed circle at point 'a'. When the inequality symbol is ≥ (greater than or equal to) or ≤ (less than or equal to), the boundary point 'a' is a solution. The closed circle visually represents this inclusion. Shade to the right for '≥' and to the left for '≤'. The Sign-Flipping Rule If you multiply or divide both sides of an ine...