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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

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Math 010: Chapter 6

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  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

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