1 / 26

Math 010: Chapter 6

Math 010: Chapter 6. October 28, 2013. Announcements. Excellent job on Exam #2 Exam #3 will be on Monday, November 18 More challenging this time All HW problems are fair game for exam questions Topics: First-degree equations Translating sentences into equations

clare
Download Presentation

Math 010: Chapter 6

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. Math 010: Chapter 6 October 28, 2013

  2. Announcements • Excellent job on Exam #2 • Exam #3 will be on Monday, November 18 • More challenging this time • All HW problems are fair game for exam questions • Topics: • First-degree equations • Translating sentences into equations • Graphing on the coordinate (x, y) plane • Unit & rate conversions (the Metric System) • Ratios, rates, and proportion

  3. 6.2 Equations: ax + b = c • Remember our goal, to get the variable alone • Take care of the constant term first by adding or subtracting • Next take care of the variable term • 7p – 2 = 26 • Constant term is -2 • Add 2 to both sides • 7p = 28 • Now divide each side by 7 • p = 4

  4. -7p + 6 = -8 • Take care of constant term first • Subtract 6 from both sides • What is -8 – 6 ? • -7p = -14 • Next, divide each side by -7 • Negative divided by negative is… • p = 2

  5. -41 = 7 – 8v • Don’t let the order confuse you, we still take care of the constant term first. • Subtract 7 from both sides. • -48 = -8v • Remember, negative or minus signs on the left of a term stay with that term. • Divide each side by -8 • 6 = v

  6. 6.3 First-degree equations • Need to simplify to obtain form ax + b = c • 4x + 3 = 2x + 9 • Get all variable terms on one side • Subtract 2x from both sides. • 2x + 3 = 9 • 2x = 6 • x = 3

  7. 6z + 5 = 3z + 20 • Try this one on your own • Get all “z” terms on one side • Subtract 3z from both sides • 3z + 5 = 20 • 3z = 15 • z = 5

  8. 2n – 3 = 5n - 18 • All variable terms need to be on one side. • Use your judgment to see which side would work best. • Rule of thumb: the smaller (or negative) variable term should move to the other side. • Subtract 2n from each side • -3 = 3n – 18 • 15 = 3n • 5 = n

  9. 2m + 3 = 23 – 8m • Try by yourself first • We will move the negative variable term. • 10m + 3 = 23 • 10m = 20 • m = 2

  10. 7 – 4a = 2a • Try by yourself • 7 = 6a • Need to divide each side by 6 • Division will get a fraction • I want a fraction here, NOT a decimal • = a

  11. 8 – 3m = 8m - 14 • Try • Move the -3m by addition • 8 = 11m – 14 • 22 = 11m • 2 = m

  12. 5a + 3 = 3a + 10 • Try • Which variable term did you decide to move? • 2a + 3 = 10 • 2a = 7 • Divide each side by 2 and get a fraction • a =

  13. 3(4y + 5) = 25 • Use the distributive property. Try this one • 12y + 15 = 25 • 12y = 10 • y =

  14. 5(3z – 2) = 8 • Try • 15z – 10 = 8 • 15z = 18 • z = • z =

  15. -2(4x + 1) = 22 • Try • Remember the negative sign distributes • -8x – 2 = 22 • -8x = 24 • x = -3

  16. 6.4 Translating Sentences to Equations • Using your skills from verbal -> variable expressions • One new thing to remember: “is” means “equals” • “A number” is your unknown variable • You pick the letter • Six less than a number is five. Find the number. • x – 6 = 5 • x = 11

  17. The sum of a number and twelve is twenty. • Try it out • n + 12 = 20 • n = 8

  18. The product of a number and eight is negative forty. • Try • 8x = -40 • x = -5

  19. Equations with fractions • Two-thirds of a number is 8. • Of means times • To “get rid” of a fraction, multiply by its reciprocal • = • = = = 12 • x = 12 is the final answer

  20. Three-fifths of a number is negative thirty. • Try it out • Reciprocal of is • = • = = = -50 • Final answer: n = -50

  21. 6.5 The Coordinate System • Points (x, y) • x horizontal, y vertical • Know how to identify each quadrant by Roman numeral • QI: both x and y positive • QII: x negative, y positive • QIII: both x and y negative • QIV: x positive, y, negative

  22. Plotting points • Plot the point (5, 2) • 5 is x (horizontal), 2 is y (vertical) • Start at the origin… (5, 2)

  23. Plot (4, -5) (4, -5)

  24. Plot (-3, -1) (-3, -1)

  25. 6.6 Graphs of Straight Lines • The easy way to graph straight lines • Pick 2 points for x and plug them in to the equation • Now you have y-coordinates • Plot the points & connect them with a line • Example: graph y = 2x – 4 on worksheet/quiz • One point: x = 0; y = 2(0) – 4 = 0 - 4 = -4 • So we have (0, -4) • Second point: x = 2; y = 2(2) – 4 = 4 – 4 = 0 • So we have (2, 0) • Plot the two points on your worksheet and connect them

  26. Worksheet is today’s quiz • Do your best – complete all problems #1-20 • Leave when you’re done! • Next class we will cover new material & real-life applications

More Related