Interval Notation You will learn how to write

Interval Notation -You will learn how to write inequalities in interval notation.

Inequality ? Verbally x is less than 3 x is greater than or equal to -4 x is greater than or equal to -5 and less than 8 x is less than 4 or greater than or equal to 7

Graphically: -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Interval Notation Uses brackets to show inclusion - replaces ≤ and ≥ [ or ] Uses parenthesis to show no inclusion -replaces < and > ( or ) Always Work From Left To Right Or Smallest To Largest

Interval Notation -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Classwork • Interval Notation worksheet

Absolute Value ? The absolute value of a number x, written |x|, is the distance the number is from 0 on a number line. The absolute value of a number is always nonnegative.

When working with absolute value equations and inequalities, always write it in a piecewise notation: split the absolute value expression into a positive and a negative version. The absolute value equation |ax + b| = c, where c > 0, is equivalent to the compound statement (ax + b) = c or -(ax + b) = c Why is c>0?

Example Remember to isolate absolute value and check for extraneous solutions

Inequalities The absolute value inequality |ax + b| < c, c > 0 is equivalent to the compound statement (ax + b) < c and –(ax + b) <c The absolute value inequality |ax + b| > c, c > 0 is equivalent to the compound statement (ax + b) > c or -(ax + b) > c

Example

Example

Checkpoint Solve and graph the following inequalities. Rewrite the problems in a piecewise notation first. 1. 2.