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Please open your laptops, log in to the MyMathLab course web site, and open Daily Quiz 8. • IMPORTANT NOTE: If you have time left out of your five minutes after you finish the two problems on this quiz, use it to check your answers before you submit the quiz! • A scientific calculator may be used on this quiz. • Remember to turn in your answer sheet to the TA when the quiz time is up. Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your notetaking materials. Section 2.9 Linear Inequalities, Part 2 Compound Inequalities A compound inequality contains two inequality symbols. Example: 0 4(5 – x) < 8 This means that 0 4(5 – x) and 4(5 – x) < 8 must both be true. Interval Notation for Compound Inequalities: • Inequality: -5 < x < -2 – The interval notation (-5,-2) represents all the numbers in between -2 and -5, excluding -2 and -5. • Inequality: -5 < x ≤ -2 – The interval notation (-5,-2] represents all the numbers in between -2 and -5, including -2 and excluding -5. • Inequality: -5 ≤ x < -2 – The interval notation [-5,-2) represents all the numbers in between -2 and -5, excluding -2 and including -5. • Inequality: -5 ≤ x ≤ -2 – The interval notation [-5,-2] represents all the numbers in between -2 and -5, including -2 and -5. Example from today’s homework: ( 7,1) Example Graph: 2 x 5 How would you write this in interval notation? Answer: (-2, 5] To solve a compound inequality, perform operations simultaneously to all three parts of the inequality (left, middle, and right) until you get the variable isolated by itself in the middle. Example: Solve the inequality 9 < z + 5 < 13 , then graph the solution set and write it in interval notation. 9 < z + 5 < 13 9 – 5 < z + 5 – 5 < 13 – 5 4< z < 8 Graph: Interval notation: (4, 8) Subtract 5 from all three parts. Example: Solve the inequality 0 4(5 – x) < 8 . Graph the solution set and write it in interval notation. 0 20 – 4x < 8 0 – 20 20 – 20 – 4x < 8 – 20 Use the distributive property. Subtract 20 from each part. – 20 – 4x < – 12 Simplify each part. 5 x >3 Divide each part by –4. 3< x 5 Reverse to put in standard form. Remember that the sign changes direction when you divide by a negative number. Graph: Interval notation: (3,5] Example from today’s homework: Example You are having a catered event. You can spend at most $1200. The set up fee is $250 plus $15 per person, find the greatest number of people that can be invited and still stay within the budget. Let x represent the number of people Set up fee + cost per person × number of people ≤ 1200 250 + 15x ≤ 1200 Example continued: You are having a catered event. You can spend at most $1200. The set up fee is $250 plus $15 per person, find the greatest number of people that can be invited and still stay within the budget. 250 15 x 1200 15 x 950 15 x 15 950 15 x 6 3 .3 The number of people who can be invited must be 63 or less to stay within the budget. The assignment on this material (HW 10) is due at the start of the next class session. Lab hours in 203: Mondays through Thursdays 8:00 a.m. to 7:30 p.m. Please remember to sign in! You may now OPEN your LAPTOPS and begin working on the homework assignment. We expect all students to stay in the classroom to work on your homework till the end of the 55minute class period. If you have already finished the homework assignment for today’s section, you should work ahead on the next one or work on the next practice quiz/test.