Day 2 - Interval Notation and Inequalities Worksheet Key 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Worksheet Key 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

©2014, viet.dang@humble.k12.tx.us Inequalities and Interval Notation ©2014, viet.dang@humble.k12.tx.us 11/20/2018 2:56 AM11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Review Determine the domain and range in Inequality Form 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Labeling Interval Notation on a Coordinate Plane >, <, or ≠ requires the dot being OPEN >, <, or = required the dot being CLOSED hole Written as: Smaller number, bigger number Brackets [ ] : DO include endpoints INCLUSIVE (think of straight line = line needed for inequality) Parentheses ( ) : DO NOT include endpoints NOT INCLUSIVE deals with infinity (think of no line = curve) 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Example 1 Determine the domain and range in Interval Notation 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Example 2 Determine the domain and range in Interval Notation 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Your Turn Determine the domain and range in Interval Notation 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Example 3 Determine the domain and range in Interval Notation 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Example 4 Determine the domain and range in Interval Notation 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Your Turn Determine the domain and range in Interval Notation 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Graphing Interval Notation On a Number Line Interval notations involve the symbols [ and ] are used to include an endpoint in an interval, and the symbols ( and ) are used to exclude an endpoint from an interval Brackets [ ] : DO include endpoints INCLUSIVE (think of straight line = line needed for inequality) Parentheses ( ) : DO NOT include endpoints NOT INCLUSIVE deals with infinity (think of no line = curve) Written as: Smaller number, bigger number Infinity always deals with parenthesis 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Example 5 Write the set x > 5 in Interval Notation and graph it on a number line 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Example 6 Write the set x < 4 in Interval Notation and graph it on a number line 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Example 7 Write the set –2 < x < 5 in Interval Notation and graph it on a number line 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Your Turn Write the set x > 0 in Interval Notation and graph it on a number line 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Example 8 Express the interval (–∞, 10) as an inequality using the variable x. 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Your Turn Express the interval [10, ∞) as an inequality using the variable x. 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Steps Isolate the x where the variable in on the left side Solve as if it was EQUAL to 0. These values are called critical values. FOLLOW THE ARROW Plot the critical values on a number line and graph. Please always label zero. 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Example 9 Solve x – 4 < –3, write the answer in Inequality form and graph on a number line 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Example 10 Solve 5x – 6 < 4x – 4, write the answer in Inequality form and graph on a number line 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Your Turn Solve 5x + 3 > 4x + 5, write the answer in Interval Notation and graph on a number line 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Rule When we negative divide, we must flip the sign. 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Example 11 Solve –3/4x > 18, write the answer in Interval Notation, and graph on a number line When we negative divide, we flip the sign 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Example 12 Solve –5(x – 1) < 10, write the answer in Interval Notation and graph on a number line When we negative divide, we flip the sign 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Example 13 Solve 4(x – 3) > 9(x + 1), write the answer in Interval Notation 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Your Turn Solve 3(x + 1) < 5(x – 2), write the answer in Interval Notation 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities

Day 2 - Interval Notation and Inequalities Assignment Worksheet 2 11/20/2018 2:56 AM Day 2 - Interval Notation and Inequalities