Graph solutions to compound inequalities (Tutorial only)

Learning Objectives Define a compound inequality and differentiate between 'and' (intersection) and 'or' (union) statements. Solve compound inequalities containing the word 'and'. Solve compound inequalities containing the word 'or'. Accurately graph the solution set of an 'and' inequality on a number line using correct endpoint notation (open/closed circles). Accurately graph the solution set of an 'or' inequality on a number line using correct endpoint notation. Interpret a graph of a compound inequality and write the corresponding algebraic statement. What's the acceptable temperature range for your phone to operate safely? 📱 A compound inequality can describe that exact range! In this tutorial, you'l...

TermDefinitionExample Compound InequalityTwo or more inequalities joined together by the word 'and' or the word 'or'.x > 3 AND x ≤ 7 is a compound inequality. Another example is x < 0 OR x ≥ 5. Intersection ('and')The set of solutions that make BOTH inequalities in a compound statement true. The graph is the region where the individual graphs overlap.For x > -2 AND x < 4, the number 1 is a solution because it is both greater than -2 and less than 4. The number 5 is not, because it is not less than 4. Union ('or')The set of solutions that make AT LEAST ONE of the inequalities in a compound statement true. The graph includes all parts of both individual graphs.For x < 1 OR x > 6, the number 0 is a solution because it is less than 1....

Graphing 'And' Inequalities (Intersection) If a < x < b, the graph is a single line segment between a and b. If a ≤ x ≤ b, the graph is a single line segment including a and b. An 'and' inequality can often be written as a three-part inequality, like -1 ≤ x < 4. To graph it, you place circles on the endpoints (-1 and 4) and shade the region BETWEEN them. The type of circle (open or closed) depends on the inequality symbol. Graphing 'Or' Inequalities (Union) If x < a OR x > b, the graph consists of two separate rays pointing in opposite directions. An 'or' inequality represents two separate conditions. You graph the solution to the first inequality and the solution to the second inequality on the same number line. The fin...