1 / 33

Chapter 3 Now You Can Solve Problems instead of just creating them!

Chapter 3 Now You Can Solve Problems instead of just creating them!. Intro to Equations. Equation Can be Numerical or Variable Has an equals sign or >, <. 9+3=12 3x-2=10. True or False. A true equation x+8=13 If x = 5 then 5+8= 13 Note: this is true. True or False.

kessie-shaffer
Download Presentation

Chapter 3 Now You Can Solve Problems instead of just creating them!

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 3Now You Can Solve Problems instead of just creating them!

  2. Intro to Equations • Equation • Can be Numerical or Variable • Has an equals sign or >, <. • 9+3=12 • 3x-2=10

  3. True or False A true equation x+8=13 If x = 5 then 5+8= 13 Note: this is true

  4. True or False • False Equation • If 9-2y=49 • So if we substitute 6 in for y • Then 9-2*6=49 • This is a lie!

  5. Solutions • A solution to an equation is a number that make the equation true. • For example: • Is -2 a solution of 2x-5=x2-3 • Lets find out by subbing in -2 • 2*(-2)-5 = (-2)2-3 • -4-5 = 4-3 • 1 = 1

  6. More examples • Is -4 a sol’n of 5x-2=6x+2 • 5x-2=6x+2 • 5(-4)-2 = 6(-4)+2 • -20 -2 = -24 + 2 • -22= -22 • YES!

  7. Even more examples • Is -4 a sol’n of 4+5x = x2-2x • 4+5x = x2-2x • 4+5(-4)=(-4)2-2(-4) • 4+(-20)=16-(-8) • -16=24 • NO!

  8. Give it a try • Is (1/4) a solution to 5-4x=8x+2? • Is 5 a solution of 10x-x2=3x-10

  9. Answers to you try it

  10. Try a Few Harder Ones • Is -6 a solution of 4x+3=2x-9 • Yes • Is (-2/3) a solution of 4-6x=9x+1 • No • Is -5 a solution of x2=25 • Yes’m

  11. Opposites • Remember: solving algebraic equations is all about opposites. • i.e. do the opposite of the whatever the mathematical operation is.

  12. Solving Stuff • What you want at the end of all your work • The variable to = a constant • Like y=5 • What's the opposite of: • Addition • Subtraction • Multiplication • Division • Exponents • Square Roots

  13. Square Roots • Break it down • Examples: • Square roots of 49, 18, 27 • You try: • Square roots of 44, 96, 45

  14. Back to where we were • First form • X+a=b • X+3=5 • Try to get simplify first (PEMDAS) • Try to isolate the variable • Do the opposite • X+3 =5 -3 -3 • X =2

  15. Example • Y+3/4=1/2 • -3/4 -3/4 • Y = -1/4 • Check your answer • Sub in what you found for Y into the original equation • Does -1/4 +3/4 = ½ • You Bet!

  16. Things are what they appear? • 3=T+2.5 • It’s the same thing– get everything away from the variable. • 3=T+2.5 • -2.5 -2.5 • 0.5=T • Check your answer

  17. Try These • 5 = x + 5 • x=0 • X-(1/4) = 5/6 • X= 13/12

  18. The second type • Form ax=b • 2x=6 • What’s the operation between the 2 and the x? • What's the opposite? • Do it! • 2x=6 • 2 2 • x=3

  19. More examples • x/4=-9 • Division • So Multiply • (x/4)*4 = -9 *4 • X=-36

  20. Tricky Problems • Ex1: 3x/4=5 • For fractions, Multiply by the reciprocal! • In this case, multiply by 4/3 • (4/3) *(3x/4) = 5*(4/3) • X=20/3 • Ex2: 5x-9x=12 • -4x=12 • divide by -4 • X=-3

  21. You try it • -2x/5 = 6 • -15 • 4x-8x = 16 • -4 • 8 = (3/4)x • 32/3 • 2z = 0 • 0

  22. Percent Problems • Basic format • Percent * Base = Amount • Figure out which 2 they are giving you. • Key words • Of means multiply • Is means equals

  23. Examples • 20% of what number is 30? • You are given the Percent and the amount • 20%*B=30 • 20% must be changed to a decimal • 0.20*B=30 • Divide by 0.2 • B=150

  24. Point of Interest? Ex: During a recent year, nearly 1.2 million dogs or litters were registered with the AKC?!. The lab retriever was the most popular with 172,841 registered. What percent of the registrations were labs? Round to the nearest tenth of a percent. PS- Dogs are considered food in some southeasters Asian countries. I heard labs are the tastiest. What's given? B and A not P P*(1,200,000)=172,841 Divide by 1,200,000 P = 0.144 Change to a percent = 14.4%

  25. You try it • 18 is 16.333% of what number? • 108 • A telephone bill of $27.25 dollars consisted on charges for a flat rate service, direct-dialed calls, and “other.” Of the total, $3.27 was for direct-dialed calls. What percent of the telephone bill was due to direct-dialed calls? What is a direct-dialed call? • 12% • The total revenue for all football bowl games in 2000 was about $158.3 million. The Big Ten conference got $22.45 million. What percent did it get? • 14.2

  26. Usury • How to use unfamiliar formulas like: • Simply Interest • I=prt • I = interest • P=principal (not principle) • r= simple interest rate • T = time (in same units as rate!!!!)

  27. Interesting Example (HA! HA!) • Last month, Nirzwan paid $545 for a Luv-Sac and had to use his credit card. Yesterday, he got his monthly bill and had to pay $8.72 in interest. What is the annual interest rate on the card? • I=prt I = 8.72, p=545, t=1/12 • Solve and get r =0.192

  28. Uniform Motion • Factoid: When an object is in uniform motion, the speed and direction do not change. • Uniform Motion Equation: d=rt where d = distance, r = rate, t = time.

  29. Suppose… • A car travels at 75 mph for 2 hours. How far does it go? • r=75mph, t = 2 hrs • d = 75*2 = 150 miles.

  30. Rate Rate is distance divided by time Best example: mph  Miles per hour Could be anything: meters per minute, inches per year, yards per second, etc. If James jogs four miles in thirty minutes what is his jogging rate in mph? 4 divided by 30 won’t do. The 30 minutes must be changed to hours by divided by 60. Now, t = 30/60 = 0.5. Rate = 4/0.5 = 8 mph. Not bad considering he runs like a duck.

  31. Examples • Ted leaves his house at 8am and gets to work at 8:30 am. He lives 15 miles away. What is Ted’s speed? • 30 mph • Joan leaves her house and travels at an average speed of 45 kph toward her shack in the mountains 180 kilometers away. How long will it take her to get to the shack if she stops for a one hour lunch break? • 5 hours.

  32. Try it before you buy it • A plane that normally flies at 250 mph in calm air (no ducks) is flying into a headwind of 25 mph. How far can the plane fly in 3 hours. • 675 mi • Two cars start from the same point and move in opposite directions. One goes west at 45 mph, and the other goes east at 60 mph. In how many hours will the cars be 210 mi apart. Hint combine rates! • 2 hours

  33. 3.1 Homework • 1 thru 154 EOO • 163 thru 172 EOO • 14, 22, 48, 74, 96, 104, 124,144, 164, 180.

More Related