Solve advanced linear inequalities

Learning Objectives Solve multi-step linear inequalities that require distribution and combining like terms. Solve linear inequalities with variables on both sides of the inequality symbol. Solve compound inequalities involving 'and' (conjunctions) and represent the solution on a number line. Solve compound inequalities involving 'or' (disjunctions) and represent the solution on a number line. Identify and interpret special cases of linear inequalities, such as those with no solution or all real numbers as the solution. Translate and solve word problems that model advanced linear inequalities. Ever wondered how to find every possible score you could get on your final test to pass the class? 🤔 Let's find out how inequalities give you a whole range of...

TermDefinitionExample Linear InequalityA mathematical statement that compares two linear expressions using an inequality symbol (<, >, ≤, ≥). It shows that one expression is not necessarily equal to the other.3x - 5 > x + 7 Compound InequalityTwo or more inequalities joined together by the words 'and' or 'or'.-2 ≤ x + 1 < 9 (an 'and' inequality) OR 2x > 10 or x - 3 ≤ -1 (an 'or' inequality) Conjunction ('and')A compound inequality where the solution must satisfy BOTH inequalities. The solution is the intersection (overlap) of the individual solution sets.x > 3 and x < 7. The solution is all numbers between 3 and 7, written as 3 < x < 7. Disjunction ('or')A compound inequality where the solution must sat...

Addition/Subtraction Property of Inequality If a > b, then a + c > b + c and a - c > b - c. You can add or subtract the same number on both sides of an inequality without changing the direction of the inequality symbol. This is used to move terms from one side to the other. Multiplication/Division Property of Inequality (The Golden Rule) If c > 0 and a > b, then ac > bc. If c < 0 and a > b, then ac < bc. When you multiply or divide both sides of an inequality by a POSITIVE number, the inequality symbol stays the same. When you multiply or divide both sides by a NEGATIVE number, you MUST REVERSE the direction of the inequality symbol.