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1) When is a mathematical sentence called an inequality? A mathematical sentence which uses at least one of the following symbols: is less than is less than or equal to is greater than is greater than or equal to is not equal to Graph the following on a number line a. x 8 Oct 11 6:03 PM 2
2) What is an open sentence? A sentence which is neither true or false until the variable is given a value. Oct 11 8:43 PM 3
3) How do we graph inequalities on a number line? We shade the portion of the number line which makes the open sentence true. Oct 11 8:43 PM 4
4) When graphing an inequality when do we use a shaded circle? A shaded circle is used to indicate the number in the inequality also makes the open sentence true. 5) When graphing an inequality when do we use a circle? A circle is used to indicate the number in the inequality does not makes the open sentence true. Oct 11 8:44 PM 5
6) What do we call all the numbers that satisfy an inequality? The solution set of the inequality The solution interval of the inequality Oct 11 8:44 PM 6
7) What is a compound sentence? A mathematical sentence in which two statements are connected by the word and or by the word or. n -7 and n<0 n is greater than or equal to negative 7 and n is less than 0 d < 4 or d > 8 d is less than negative 4 or d is greater than 8 2 s<3 s is greater than or equal to 2 and s is less than 3 Oct 11 8:44 PM 7
8) Describe the solution set of a compound sentence which uses the word and to connect two inequalities. The intersection of the two individual solution sets of the separate statements. The numbers common to both inequalities and Feb 18 9:17 AM 8
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11) How do we read? A and B or The intersection of A and B n -7 and n<0 2 s<3 s -2 and 2 s<3 3 Oct 11 6:59 PM 10
12) Describe the solution set of a compound sentence which uses the word or to connect two inequalities. The union of the two solution sets of the separate statements Union means in one, the other, or both Take all the numbers in each separate statement and combine them 13) How do we read? The union of set A with set B d < 4 or d > 8 d < 4 d > 8 d < 4 or d > 8 Oct 11 6:53 PM 11
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AdvAlg5.1InequalitiesAndCompoundSentences.notebook 16) Oct 11 6:57 PM 13
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Which property of inequalities requires the most consideration? The multiplication property of inequalities Feb 18 9:19 AM 15
19)While solving inequalities when are we required to reverse the relation? When multiplying or dividing both sides of the inequality by a negative number we must reverse the relation (flip the inequality) Feb 18 9:19 AM 16
20) 21) After 5.6 minutes the plane will be below 20,000 feeet Feb 18 9:19 AM 17
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When two or more sentences are joined by the words and or or, a compound sentence results. The solution set to A or B is the union of the two solution sets. If the word joining them is and, the compound sentence is called a system. The solution set to A and B is the intersection of the two solution sets. If an algebraic sentence includes a single variable then its solution can be graphed on a single number line. Feb 18 9:20 AM 19
Notes 5 1 Inequalities & Compound Sentences x > 4 is an inequality that has infinite solutions. Graph them. Now graach of the following x 4 x < 4 x 4? Sep 6 7:00 AM 20
As of 1994, recorded temperatures in the state o of Michigan have ranged from a low of 51 F in o Vanderbilt ( 1934 ) to a high of 112 F in Mio ( 1936 ). Graph all the possible recorded values of the temperatures mentioned above. Sep 6 8:20 AM 21
People from age 16 to 65 can give blood at a blood bank. Write a compound inequality to describe the possible ages at which blood can be drawn. Graph the solution on a number line. Write an inequality of people who cannot give blood at a blood bank. Sep 6 8:23 AM 22
use a solid circle, point is included use an open circle, point is not included The overlapping of sets. Points that are common to both sets AND The combining or uniting of sets. OR State Street 110th Street Sep 10 8:12 PM 23
{x: 2 x 9} set builder notation The set of all x such that x is greater than or equal to 2 and less than or equal to 9 {x: x 5} {x: x >10} set builder notation The set of all x such that x is less than or equal to 5 UNION with the set of all x such that x is greater than 10 Sep 10 8:16 PM 24
#1 Graph the sales for this commission on a number line. Michael will receive a 2% commission on sales that are at least $25,000 but not over $39,000. #2 Solve and graph: 3x + 11 < 20 Sep 10 8:17 PM 25
#4 Write an inequality, solve and graph Kari owns some shares of Google. The price per share is $104.35. However, the stock has been declining by $1.37 each day. Determine the number of days it will take for the stock shares to be under $88.90. Graph the solutions. Sep 10 8:19 PM 26
#4 Graph on the number line set builder notation Sep 10 8:20 PM 27
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WS 5.1 5.10 Lesson Masters (A).pdf Feb 18 12:28 PM 43
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WS 5.1 5.10 Lesson Masters (A) KEY.pdf Nov 9 2:28 PM 47
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Attachments WS 5.1 5.10 Lesson Masters A.pdf WS 5.1 5.10 Lesson Masters A KEY.pdf