2.5 Linear Equations and Formulas:

3.6 Compound inequalities:Inverse Operations: Operations that undo another operation. Isolate: The use of inverse operations used to leave a variable by itself. Compound Inequalities: two distinct inequalities joined by the word and or the word or.GOAL:

These inequalities have the following graphs when the word and is being used:Compound inequalities:

Set Notation: {x|3 x 7}Interval: [3, 7]Compound inequalities:

Set Notation: {x| x < -2 or x 1}Interval: (-,-2)U[1, ) These inequalities have the following graphs when the word or is being used:WRITING Compound inequalities:We must be able to transform English sentences into math equations:EX:What compound inequality represents the phrase:

All real numbers that are greater than 2 and less than or equal to 6 SOLUTION: All real numbers that are greater than 2 and less than or equal to 6All real numbers greater than -2X > -2 andAll real numbers less than or equal to 6 X 6-2 < x 6

Set Notation: {x| -2 < x 6} Interval: (-2, 6] YOU TRY IT:What compound inequality represents the phrase:

All real numbers that are less than 0 or greater than 5 SOLUTION: All real numbers that are less than 0 or greater than 5All real numbers less than 0X < 0 orAll real numbers greater than 5 X > 5x< 0, x > 5

Set Notation: {x| x < 0, x > 5} Interval: (-,0) U (5, ) SOLVING Compound Inequalities:To solve inequalities we follow inverse operations just like we do to isolate a variable:EX:What are the solutions of: - 2 2m 4 < -1 SOLUTION:- 2 2m 4 < -1Given (and) 4 - 2 2m 1

or Interval: (-,-3) U (1, ) Real-World:You have taken a quiz and got 55%. You are about to take another quiz next week. If you want to pass the portion of quizzes in the class you must get an average between 70% and 79% What are the possible percentages you must get on the next quiz?Real-World: (SOLUTION)Quiz 1 = 55%Quiz 2 = x%70% and 79%Thus in order for you to obtain a passing grade in your quizzes, you must get between 85% and 103% on your next quiz? (Good Luck!!!) Real-World:A secondary 15-year old student should consume no more than 2200 calories per day. A moderately active student should consume between 2400 and 2800. An active 15-year-old student should consume between 2800 and 3200 calories per day. Model these ranges on a number line and represent them in set and interval notations. SOLUTION:A secondary 15-year old student should consume no more than 2200 calories per day.

010002000 Set: { x | 0 < x 2200} Interval: (0, 2200] 220016SOLUTION:A moderately active student should consume between 2400 and 2800 Calories per day.

010002000 Set: { x | 2400 < x 2800} Interval: (2400, 2800) 28003000240017SOLUTION:An active 15-year-old student should consume between 2800 and 3200 calories per day.

010002000 Set: { x | 2800 < x 3200} Interval: (2800, 3200) 32003000280018VIDEOS:Compoundinequalitieshttps://www.khanacademy.org/math/algebra/linear_inequalities/compound_absolute_value_inequali/v/compund-inequalitieshttps://www.khanacademy.org/math/algebra/linear_inequalities/compound_absolute_value_inequali/v/compound-inequalitiesVIDEOS:Compoundinequalitieshttps://www.khanacademy.org/math/algebra/linear_inequalities/compound_absolute_value_inequali/v/compound-inequalities-3https://www.khanacademy.org/math/algebra/linear_inequalities/compound_absolute_value_inequali/v/compund-inequalities-2CLASSWORK:

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Problems: As many as needed to master the concept.