Presentation on theme: "Please close your laptops"— Presentation transcript:
1Please close your laptops and turn off and put away your cell phones, and get out your note-taking materials.Today’s daily 5-minute quiz will be given at the end of class.
2Weekly Quiz 2 Results:Average class score after partial credit: _______ (_____ raw score)Commonly missed questions: #_______________Grade Scale
3Why you should keep taking the practice quiz until you can score at least 90%: (B+)(almost a C-)(low F)
4REMINDERS for the upcoming Test 1: Take the practice test early enough so you’ll have time to review it, retake it, come into the open lab for help if needed.Review each practice test after you submit it. (The “help me solve this” buttons will appear when you review the test.)You have unlimited attempts, so retake the practice test until you score at least 90%.If you score < 90%, come into the open lab to review your practice test with a TA (Or just take the practice test in the open lab to start with …)
5Note to teachers: You can use item analysis to see which questions your section missed most, and you can insert slides here with screen shots of those questions you want to go over in class.
8Linear InequalitiesAn inequality is a statement that contains one of the symbols: < , >, ≤ or ≥.Linear equations: Linear inequalities:x = 3 x > 312 = 7 – 3y 12 ≤ 7 – 3y
9Graphing solutions to linear inequalities in one variable Use a number line.Use a square bracket at the endpoint of an interval if you want to include the point.Use a parenthesis at the endpoint if you DO NOT want to include the point.Graph the inequality x 7:Graph the inequality x > – 4:
10Using graphs to figure out how to write a solution in interval notation: The inequality x is expressed in interval notation as (-, 7]-∞∞-∞∞The inequality x > -4 is expressed in interval notation as (-4, )
11IMPORTANT: In interval notation, ∞ and -∞ ALWAYS are enclosed by a (round bracket)NEVER by a [ square bracket].
13Addition property of inequality a< b and a + c < b + c are equivalent inequalities.Example: 2 ≤ 4 and (-3) ≤ 4 + (-3) are equivalentMultiplication property of inequalityif c is positive, then:a< b and ac < bc are equivalent inequalities,Example: 3 ≥ 1 (multiply both sides by 2); so 6 ≥ 2 is equivalent.if c is negative, then:a< b and ac > bc are equivalent inequalities,Example: 3 ≥ 1 (multiply both sides by -2); so ≤ -2 is equivalent..
14Solving linear inequalities in one variable Multiply to clear fractions.Use the distributive property (parentheses).Simplify each side of the inequality.Get all variable terms on one side and numbers on the other side of inequality (addition property of inequality).Isolate variable by dividing both sides by the number in front of the variable (multiplication property of inequality).Do not forget to change the direction of the inequality sign if you multiply or divide both sides by a negative number.
15Caution:Don’t forget that if both sides of an inequality are multiplied or divided by a negative number, the direction of the inequality sign MUST BE REVERSED.
16Example 1:-7(x – 2) - x < 4(5 – x) x x < x + 12 (use distributive property) - 8x + 14 < - 4x + 32 (simplify both sides) - 8x + 4x + 14 < - 4x + 4x + 32 (add 4x to both sides) - 4x + 14 < 32 (simplify both sides) - 4x < (subtract 14 from both sides) - 4x < 18 (simplify both sides)(divide both sides by -4)(simplify)Graph of solution ( ,)
19Something to think about: How would you graph the inequality 2 > x?What would this look like in interval notation?Note that 2 > x is equivalent to x < 2.Writing the inequality with the variable term on the left makes it easier to “see” what the graph and the interval notation should look like.Interval notation: (-∞, 2)This is an argument for working to put/keep your variables on the left side of the expression as you solve linear inequalities.
20Inequality Applications Example: Six times a number, decreased by 2, is at least 10. Find the number.1.) UNDERSTANDLet x = the unknown number.“Six times a number” translates to 6x,“decreased by 2” translates to 6x – 2,“is at least 10” translates ≥ 10.
21Example continued: 2.) TRANSLATE Six times a number 6x decreased – by 22is at least≥10
22Example continued: 3.) SOLVE 6x – 2 ≥ 10 6x ≥ 12 Add 2 to both sides. x ≥ 2 Divide both sides by 6.4.) INTERPRETCheck: Replace “number” in the original statement of the problem with a number that is 2 or greater.Six times 2, decreased by 2, is at least 106(2) – 2 ≥ 1010 ≥ 10 State: The number is 2.
23REMINDER: In interval notation, ∞ and -∞ ALWAYS are enclosed by a (round bracket)NEVER by a [ square bracket].
24Mondays through Thursdays Please remember to sign in! The assignment on this material (HW 9) is due at the start of the next class session.Lab hours in 203:Mondays through Thursdays8:00 a.m. to 7:30 p.m.Please remember to sign in!
25Please open your laptops, log in to the MyMathLab course web site, and open Daily Quiz 7. A scientific calculator may be used on this quiz. (No graphing calculators, calculator apps or notes.)Write your name, date, and section info on the worksheet handout and use this sheet for any scratch work you do for this quiz.You have 5 minutes to finish this 2-question quiz.If you finish the quiz problems in less than 5 minutes, remember to check your work and your online answers before submitting the quiz.After you submit your quiz, turn your worksheet in to the TA, and then you are free to leave.