Solve compound inequalities

Learning Objectives Define a compound inequality and differentiate between 'and' (intersection) and 'or' (union) cases. Solve compound inequalities containing the word 'and' and express the solution algebraically, on a number line, and in interval notation. Solve compound inequalities containing the word 'or' and express the solution algebraically, on a number line, and in interval notation. Correctly apply the rule for flipping the inequality sign when multiplying or dividing by a negative number within a compound inequality. Interpret the meaning of 'no solution' or 'all real numbers' as possible outcomes. Model and solve real-world scenarios using compound inequalities. To get a driver's license, you must be...

TermDefinitionExample Compound InequalityTwo or more inequalities connected by the words 'and' or 'or'.x > 3 and x ≤ 7, which can be written as 3 < x ≤ 7. Another example is x < 0 or x ≥ 5. Intersection ('and')The solution set for an 'and' inequality. It includes only the numbers that make BOTH individual inequalities true. Think of it as the 'overlap' between the two solution sets.For 'x > 2 and x < 5', the number 3 is a solution because it's both greater than 2 and less than 5. The number 6 is not, because it's not less than 5. Union ('or')The solution set for an 'or' inequality. It includes all numbers that make AT LEAST ONE of the inequalities true. Think of it as combining both so...

Solving 'And' Inequalities (Intersection) If a < x + c < b, then a - c < x < b - c To solve a three-part inequality, perform the same operation on all three parts to isolate the variable in the middle. The solution is a single range of numbers. Solving 'Or' Inequalities (Union) Solve 'ax + b < c' OR 'dx + e > f' separately To solve an 'or' inequality, solve each inequality independently. The final solution is the combination (union) of the two individual solution sets, connected by the word 'or'. The Flipping Rule If -ax > b, then x < -b/a When you multiply or divide all parts of an inequality by a negative number, you MUST flip the direction of the inequality symbol(s). For example,...