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6.1 Solving One-Step Linear Inequalities x + 8 > 1 6.2 Solving Multi-step Linear Inequalities 5x – 3 > 12 6.3 Solving Compound Inequalities -5<2x + 3 <

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Presentation on theme: "6.1 Solving One-Step Linear Inequalities x + 8 > 1 6.2 Solving Multi-step Linear Inequalities 5x – 3 > 12 6.3 Solving Compound Inequalities -5<2x + 3 <"— Presentation transcript:

1 6.1 Solving One-Step Linear Inequalities x + 8 > Solving Multi-step Linear Inequalities 5x – 3 > Solving Compound Inequalities -5<2x + 3 < Solving Absolute-value Equations and Inequalities |x-4|=8 |5x+1|+3 = Graphing Linear Inequalities in Two Variables Graph x + y > 3

2 6.6 Stem and leaf plots; mean, median, mode 6.7 Box and whisker plots

3 Ch 7 Systems of Linear Equations and Inequalities November 28 A A H 7.3 December 1 D A Quiz new7.4 5 A Penance Service Penance Service Mass 7.6 & review 9 A 12 A Chapter Review 13 A Chapter 7 Test 14 H Review for final 15 D Review for final 16 A Review for final 21 Final Exam Ch 1-7 Due Tuesday 11/ p401 12,16,18, 22,26,36,44 Due Wednesday 11/307.2 p #14,16,18,20, 26, 30,35,44,48-51 Due Thursday12/17.3 p414 #8, 14, 18, 24, 26, 30, 36, 40, 44 Due Friday 12/27.3 p414 #45-52, 56; p

4 7.1 Solving systems of linear equations by graphing: Graph-Estimate-Check y=3x-12 and y=-2x+3 (3,-3)

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8 7.1 p401 12,16,18, 22,26,36,44

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14 7.1 Solving a System of Linear Equations by Graphing 7.2 Solving a System of Linear Equations by Substitution

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16 Solve by Substitution 3x+y=5 and 2x-y=10 (3,-4)

17 Solve by Substitution 2x+6y=15 and x=2y (3,3/2)

18 Solve by Substitution x+2y=4 and –x+y=-7 (6,-1)

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20 Homework: p #14,16,18,20, 26, 30,35,44,48-51

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26 7.1 Solving a System of Linear Equations by Graphing 7.2 Solving a System of Linear Equations by Substitution 7.3 Solving Linear Systems by Linear Combination Solving by graphing can be challenging Substitution is easier than graphing, but sometimes it is not easy to isolate the variable. …let’s try Linear Combination -x+2y=-8 x+6y=-16 x+6y=-16 8y=-24 y=-3 To find x, plug in -3 into one of the equations x+6(-3) = -16 x-18=-16 x=2 solution (2, -3) Check -2+2(-3)=-8

27 Solve by linear combination: 5x-4y=3 2x+8y=-2 2(5x)-2(4y) = 2(3) (multiply first equation by 2 to get y’s to cancel) 10x -8y =6 2x + 8y = -2 12x = 4 x= 1/3 To find y: 2(1/3)+8y= -2 2/3 +8y = -2 8y=-2 2/3 8y= -8/3 y=-1/3 Check: 5(1/3) -4(-1/3) = 3 2(1/3) +8(-1/3)= -2 Solution: (1/3, -1/3) Solve by linear combination: 3x-6y= -12-x+3y=6 3x -6y= x+9y= 18 (multiply each term by 3) 3y=6 y=2 To find x: 3x-6(2)= -12 3x=0 x=0 Check: -(0) +3(2) = 6 3(0)-6(2)=-12 Solution: (0,2)

28 Solve by linear combination: 2u=4v+8 3v=5u-13 2u-4v=8 -5u+3v= -13 (reorganize so variables on same side) 10u – 20v =40 (to get “u” to cancel, multiple top equation by 5) -10u +6v = -26 (to get “u” to cancel, multiple bottom equation by 2) -14v=14 v=-1 2u=4(-1)+8 (to find “u”, plug in v=-1 into one of the equations) 2u=4 u=2 Check: 2(2)=4(-1)+8 3(-1)=5(2)-13 Solution: (u,v)=(2, -1)

29 2. When the 2 nd equation was multiplied by -2, 4y(-2) is not=8y 3. When adding 9x+7x, it is not=2x

30 7.3 p414 #8, 14, 18, 24, 26, 30, 36, 40, 44 3x = 6 (add equations, y’s cancel) x= 2 2-y=2 (insert 2 for x in 2 nd equation) -y=0 so y=0 Check 3(2)= 6 and 2-0=2 Solution: (2, 0) -1/2g =4 (add equations, h’s cancel) g=-8 (solve for g) (1/2)(-8)+h=2 (insert -8 for g in 1st equation) -4+h=2 h=6 Check: (1/2)(-8)+6=2 ; -(-8)-6=2 Solution: (-8, 6)

31 7.3 p414 #8, 14, 18, 24, 26, 30, 36, 40, 44 -x-3y=-3 (multiply 1 st equation by -1) x+6y=3 3y=0 y=0 x+3(0)=3 (insert 0 for y in 1 st equation) x=3 Check: 3+3(0)=3; 3+6(0)=3 Solution: (3,0) 9x -3z =20 -9x-18z=-6 (multiply 2 nd equation by -3) -21z=14 z=-2/3 9x-3(-2/3)=20 (insert -2/3 for z in 1 st equation) 9x+2=20 9x=18 x=2 Check: 9(2)-3(-2/3)=20 3(2)+6(-2/3)=2 Solution: (2, -2/3)

32 7.3 p414 #8, 14, 18, 24, 26, 30, 36, 40, 44 3b +2c=46 -3b-15c=-33 (multiply 2 nd equations by -3) -13c=13 c=-1 3b+2(-1)=46 3b=48 b=16 Check: 3(16)+2(-1)=46 5(-1)+16=11 Solution: (16, -1) 0.1g-h=-4.3 (subtract -4.3 from both sides) -0.2g+h=3.6 (reorganize & multiply by -1) -0.1g=-0.7 g=7 0.1(7)-h+4.3=0 (insert 7 for g in 1 st equation).7-h+4.3=0 5=h Check: 0.1(7)-5+4.3=0 3.6=-0.2(7)+5 Solution: (7,5)

33 Solve by linear combination: 4a+b=0 (reorganize 1 st equation) 1a-b=5 (reorganize 2 nd equation) 5a=5 a=1 3(1)+9b=8b-1 (insert 1 for a in 1 st equation) 4=-b b=-4 Check: 3(1)+9(-4)=8(-4)-1 5(1)-10(-4)=4(1)-9(-4)+5 Solution: (1,-4) 1.5v-6.5w= v-6w=9 (multiply 2 nd equation by -3) -12.5w=12.5 w=-1 0.5v+2(-1)=-3 0.5v-2=-3 0.5v=-1 v=-2 Check: 1.5(-2)-6.5(-1)= (-2)+2(-1)=-3 Solution: (-2,-1)

34 y=(9/7) x y=-3x+12 7y=9x (multiplied 1 st equation by 7) -7y=21x-84 (multiplied 2 nd equation by -7) 0=30x-84 30x=84 x=14/5 y=-3(14/5)+12= -8 2/5 +12= 3 3/5 solution: (14/5, 18/5) Check: 18/5 = (9/7) (14/5) 18/5 = -3(14/5) + 12

35 p414 #45-52, 56; p )s=speed in still air w=wind speed s-w =300 s+w=450 2s=750 s=375 If s=375, then 375-w=300 w=75 Check: = = mph =speed of plane 75mph =speed of wind

36 p414 #45-52, 56; p ) boat traveled upstream 8 miles in 1 hour boat traveled downstream 8 miles in ½ hour b-w=8 boat speed-speed of water = 8 mph b+w=16 boat speed +speed of water=16 mph 2b=24 b=12 w=4 Boat was traveling at 12 mph, water was going 4mph.

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38 Quiz Prep

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44 Ch 7 Systems of Linear Equations and Inequalities November 28 A A H 7.3 December 1 D A Quiz new7.4 5 A Penance Service Penance Service Mass 7.6 & review 9 A 12 A Chapter Review 13 A Chapter 7 Test 14 H Review for final 15 D Review for final 16 A Review for final 21 Final Exam Ch 1-7 Due Monday 12/5 7.4 p421 #12, 20, 28, 42, 48; chapter 1 summary p54-56 Due Tuesday 12/6 7.5 p429 #12-17,18,24,30,43-46; chapter 2 review Due Wednesday 12/7 7.6 p435 #9-14, 26; chapter 3 review Due Thursday 12/8 7.6 p435 # 37,43; chapter 4 review Due Friday 12/9 chapter 7 review p440 #2-32 (pick one in each section)

45 7.4 Applications of Linear Systems

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47 What would you use to solve this system of equations? Why?

48 Total cost regular + total cost premium =$32.75 Cost premium = cost regular +.2 Regular gas amount (cost) + premium gas amount (cost)=$ c + 15(c+.20) = c +3 = c = c=$1.19 cost for regular, $1.39 cost for premium To check: 10(1.19) + 15( )=32.75 Cr+cp=32.75 Cp=cr+.2

49 2x – y = 3 2x - 3 = y 4x + 3(2x-3) = 21 4x + 6x – 9 = 21 10x = 30 x = 3 4(3) + 3y = y = 21 3y = 9 y = 3 (3,3) Check: 2(3) -3 = 3 4(3) + 3(3) = 21

50 -x + -2y = -2 (multiply 1 st equation by -1) x + 4y = -2 2y =-4 y = -2 x + 2(-2) = 2 x=6 (6, -2) Check: 6 + 2(-2) = (-2) = -2

51 -4{1.5x-2.5y=8.5} multiply 1 st equation by -4 -6x+10y=-34 6x+30y=24 (add both equations to cancel x’s) 40y=-10 y= x+30 (-.25)=24 6x-7.5 =24 6x =31.5 x= 5.25 ?(5.25, -.25) Check: 1.5 (5.25)-2.5(-.25)=8.5 6(5.25)+30(-.25)=24 Solution: (5.25, -.25)

52 y=4x + 14 y=6x + 8 6x+8=4x+14 (substitution) 2x=6 x=3 (at 3 years they are equal) y=4(3)+14=26 inches YearHemlock(+4)Spruce (+6) (3,26) y=6x+8 y=4x+14

53 Chapter 1 Summary

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55 *2 equations, same slope, different y=intercepts, no solution

56 *2 equations, same slope, same y=intercepts, infinite # of solutions

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62 7.5 p429 #12-17,18,24,30,43-46; chapter 2 review

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65 Weight of necklace = weight of 30 small beads + weight of 6 large beads Weight of bracelet = weight of 10 small beads + weight of 2 large beads 3.6 = 30x + 6y 1.2 =10x + 2y -3.6=-30x-6y (multiply 2 nd equation by -3) 0=0 They are equivalent equations, so we cannot use them to solve the problem.

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67 Chapter 2 Summary

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73 7.6 p435 #9-14, 26; chapter 3 review

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