1 / 75

Solving Linear Equations

Solving Linear Equations. Algebra—Chapter 3. Section 3.1. Solving Equations Using Addition & Subtraction. Equivalent equations: Equations with the same solutions Apply transformations to create equivalent equations Goal: apply transformations to isolate the variable.

marnie
Download Presentation

Solving Linear Equations

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. Solving Linear Equations Algebra—Chapter 3

  2. Section 3.1 • Solving Equations Using Addition & Subtraction

  3. Equivalent equations: • Equations with the same solutions • Apply transformations to create equivalent equations • Goal: apply transformations to isolate the variable

  4. Transformations that we can use: • Add same number to each side • Subtract same number from each side • Simplify one or both sides • Interchange the sides • “Balance the scale”

  5. More definitions! • Inverse operations: • Operations that undo each other • Linear equation:

  6. Solving equations • x – 5 = – 13 • – 8 = n – (-6)

  7. Solving equations • 11 = r – 4 • t – 2 = 6 • 19 – (-y) = 25

  8. Model a real-life problem • Your bank balance is $42. If you write a check to buy a pair of shoes, your balance would be – $5. • Use an equation to model the cost of the shoes.

  9. Assignment • Section 3.1 • Page 135 • 21-44 All

  10. Section 3.2 • Solving Equations Using Multiplication and Division

  11. More transformations that we can use: • Multiply each side by same non-zero number • Divide each side by same non-zero number

  12. Examples:

  13. Examples

  14. Properties of equality • Addition property • If a = b, then a + c = b + c • Subtraction Property • If a = b, then a - c = b - c • Multiplication Property • If a = b, then a • c = b • c • Division Property • If a = b, and c ≠ 0, then a ÷ c = b ÷ c

  15. Ratios: • If two quantities are measured in the same units, then the ratio of a to b is

  16. Similar triangles: • Have equal corresponding angles • Ratio of lengths of corresponding sides are equal B E D F A C

  17. Assignment • Section 3.2 • Page 141-143 • 14-46 even, 48-53 all, 58, 59

  18. Section 3.3 • Solving Multi-step Equations

  19. Multi-step equations • Involve 2 or more transformations • Simplify one or both sides (if necessary) • Use inverse operations to isolate variable

  20. Solve:

  21. Solve:

  22. Assignment: • Section 3.3 • Page 148 • 16-40

  23. Multi-step equations—Day 2

  24. Consecutive integers • The sum of two consecutive integers is 25. What are the two integers?

  25. Using formulas • Use the formula to convert 102 degrees Fahrenheit to Celsius

  26. Assignment • Section 3.3 • P 149-150 • 46-65

  27. Section 3.4 • Solving Equations with Variables on Both Sides

  28. Collect all the variables on one side • Either left or right, no difference

  29. 6x + 22 = -3x + 31 • 64 – 12w = 6w

  30. Many solutions—or—no solution • Identity: • Examples: 3(x+2) = 3x + 6 x + 2 = x + 4

  31. Solve:

  32. Assignment • Section 3.4 • Page 157 • 12-34 all

  33. Solving Equations with Variables on Both Sides—Day 2

  34. Member-ship fee Visits to the gym Cost per visit Member-ship fee Visits to the gym Cost per visit + = + * * • A gym offers two packages for yearly membership. The first plan costs $50 to be a member. Then each visit to the gym is $5. The second plan costs $200 for a membership fee plus $2 per visit. Which membership is a better deal?

  35. Unit Analysis: • Check the units to make sure your units match

  36. Find resulting unit of measure • (Dollars per hour) * (hour) • (years)*(people per year)

  37. Assignment • Section 3.4 • Practice A

  38. Section 3.5 • Linear Equations and Problem Solving

  39. Problem solving strategies • Draw a diagram • Use a table/graph as a check

  40. Draw a Diagram • A page of pictures for a yearbook is 8.5 inches by 11 inches. • The top margin is .75 inches, and the bottom is 1.25 inches. • The space between the pictures is 3/16 inch. • How high can each picture be to fit seven down the length of the page?

  41. Use a table to check • At West High School, 362 students take Spanish. • This number has been increasing at a rate of 20 per year. • The number of students taking French is 259 and has been decreasing at a rate of about 3 per year. • At these rates, when will there be two times as many students taking Spanish as taking French?

  42. Using a graph as a check • Horizontal axis • Vertical axis

  43. Jim can run 11 ft/sec and Sarah can run 13 ft/sec. How far ahead of Sarah must Jim be to fall behind Sarah in the first 15 seconds that they run?

  44. Assignment • Section 3.5 • Page 163-165 • 6-21 all, 31-39 odd

  45. Section 3.6 • Solving Decimal equations

  46. Round-off error: • Exact answer isn’t always practical • Example: Restaurant bill is 12.95, want to split evenly 3 ways. • 3x=12.95

  47. If four people are sharing the cost of a monthly phone bill of $58.25, what is each person’s share of the bill?

  48. Equations with decimals: • Same methods as without decimals • Round answer (usually to nearest hundredth)

  49. Example: • Round to nearest hundredth 9.92x – 6.13 = 5.96 – 7.28x

More Related