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Review 4.6-4.7

Review 4.6-4.7. Solve each equation or inequality. 1. 2. Multiply every term by 12. b = 2, -5. Solve each equation or inequality. 3. 4. USE QUADRATIC FORMULA. w = 2/5, -1. What values go on your number lines??. 2/5, -1, 0, and 1. Example : Solve. LCM : 2x

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Review 4.6-4.7

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  1. Review 4.6-4.7

  2. Solve each equation or inequality 1. 2. Multiply every term by 12 b = 2, -5

  3. Solve each equation or inequality 3. 4. USE QUADRATIC FORMULA w = 2/5, -1 What values go on your number lines?? 2/5, -1, 0, and 1

  4. Example: Solve. LCM: 2x Multiply each fraction through by the LCM Check your solution!

  5. Solve. LCM: ? LCM: (x+1) ? Check your solution! No Solution!

  6. Solve. Factor 1st! LCM: (x+2)(x-2) Check your solutions!

  7. Example: Solve. Check your solutions!

  8. Last Example: Solve. Check your solutions!

  9. Solve Check your solution. The LCD for the three denominators is Original equation Multiply each sideby 24(3 – x). Example 6-1a

  10. 6 1 1 1 1 1 Simplify. Simplify. Add. Example 6-1b

  11. Check Original equation Simplify. Simplify. Example 6-1c The solution is correct.

  12. Answer: The solution is –45. Example 6-1d

  13. Solve Answer: Example 6-1e

  14. Solve Check your solution. The LCD is Original equation p – 1 1 Multiply by the LCD, (p2 – 1). 1 1 Example 6-2a

  15. DistributiveProperty Simplify. Simplify. Add(2p2 – 2p + 1)toeach side. Example 6-2b

  16. Divide eachside by 3. Factor. Zero ProductProperty or Solve eachequation. Example 6-2c

  17. Check Original equation Simplify. Simplify. Example 6-2d

  18. Original equation Simplify. Example 6-2e Since p = –1 results in a zero in the denominator, eliminate –1. Answer: The solution is p = 2.

  19. Solve Answer: Example 6-2f

  20. Decompose this into partial fractions 5.

  21. Solve Related equation Example 6-5a Step 1 Values that make the denominator equal to 0 are excluded from the denominator.For this inequality the excluded value is 0. Step 2 Solve the related equation.

  22. Multiply each side by 9s. Simplify. Add. Divide each side by 6. Example 6-5b

  23. Step 3 Draw vertical lines at the excluded value and at the solution to separate the number line into regions. Example 6-5c Now test a sample value in each region to determine if the values in the region satisfy the inequality.

  24. Test is a solution. Example 6-5d

  25. Test is not a solution. Example 6-5e

  26. Test is a solution. Example 6-5f

  27. Answer: The solution Example 6-5g

  28. Solve Answer: Example 6-5h

  29. Solve each equation or inequality 6. 7. x = 7 No real solution

  30. Solve each equation or inequality 8. 9. k = 7 m = -13

  31. Solve each equation or inequality 10. t > 14

  32. 11.) Find the upper and lower bound of the zeros of: Upper = 4 Lower = -1

  33. Approximate the real zeros of each functions 12. 13. Between 1 and 2 Between -1 and 0 Between 2 and 3

  34. Approximate the real zeros of each functions 14. 15. Between -5 and -4, -1 and 0, 1 and 2 No real zeros

  35. 16.) Find the number of positive, negative, and imaginary: Pos. 2 or 0 Neg. 1

  36. 17.) Find the possible rational roots:

  37. Find the remainder of each division. Then state whether the binomial is a factor? 18. 19. Remainder = 55 Not a factor Remainder = 18 Not a factor

  38. 20.) Use synthetic division to divide:

  39. Graph each equation or inequality: 21. 22.

  40. Solve each equation or inequality 23. 24.

  41. Solve each equation by completing the square: 25. 26.

  42. 27.) Find the discriminant of the function given and describe the nature of the roots. Discriminant = 73 2 distinct real roots

  43. Write the polynomial equation of least degree have the roots: 28.)1, -1, 0.5

  44. Find the roots of each equation: 29. 30.

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