Math 021

* Interval Notation is a way to write a set of real numbers. The following are examples of how sets of numbers can be written in interval notation: Graph InequalityInterval (-2, 3] (-∞, 3) [-2, ∞)

InequalityGraphInterval a. b. c. d.

* Solving Linear Inequalities * Solving linear inequalities is similar to solving linear equations. Replace the inequality with an equal sign and solve using the same rules as solving linear equations. When solving, there is a rule of inequalities that must be followed: * If a,b, and c are real numbers and c < 0: If a bc If a > b, then ac < bc * In other words multiplying or dividing an inequality by a negative number flips the inequality.

* Examples – Solve, graph, and write each inequality in interval notation: * a. 3x – 1 < 11 * b. 2(x + 3) ≥ x + 4 * c. 4(3x – 1) ≤ 10(x + 1) * d. 4x x > 3 + 2x + 6 * e. -6x - 2 ≤ 10 * f. 30 < -5x

* Solving Compound Inequalities * A compound inequality is any inequality that contains two or more inequality symbols. * A union between two inequalities is all the set of all elements that belongs to either inequality. * Keyword for union is Or * An intersection of two inequalities is the set of all elements that belong to both inequalities. * Keyword for intersection is And