Algebra 1: Module 2: 02.06 Compound Inequalities

Absolute value inequalities

Problems that involve ranges

Conjunctions

Two inequalities connected by the word "and." ---------- ~Solutions to conjunctions have to fit the conditions of both inequalities. ~Conjunctions may be written separately like x > −3 and x < 3. ~Conjunctions may be written together like −3 < x < 3. ~If the two inequalities have no intersection in their solutions, then there are "no solutions." The graph of this is a blank number line.

Disjunctions

Two inequalities connected by the word "or." ------- ~Solutions to disjunctions can fit the conditions of either of the inequalities. ~Disjunctions should be written separately like x < −3 or x > 3. ~If the solutions to a disjunction cover the entire number line, the solutions are "all real numbers." The graph of this is a number line that is shaded completely.

If the absolute value inequality contains a greater than symbol (≥, >):

Write two separate inequalities to solve. A. Drop the absolute value bars. B. Create a second inequality with the flipped inequality symbol, opposite value, and the word "or" in between. 2.)Solve the two inequalities. 3.)Draw the graph with two parts in opposite directions

If the absolute value inequality contains a less than symbol (≤, <):

1.)Write two separate inequalities to solve. A. Drop the absolute value bars. B. Create a second inequality with the flipped inequality symbol, opposite value, and the word "and" in between. 2.)Solve the two inequalities. 3.)Draw the graph between two values.