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Lesson 6 Contents

Lesson 6 Contents. Example 1 Solve a Rational Equation Example 2 Elimination of a Possible Solution Example 3 Work Problem Example 4 Rate Problem Example 5 Solve a Rational Inequality. Solve Check your solution. The LCD for the three denominators is. Original equation.

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Lesson 6 Contents

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  1. Lesson 6 Contents Example 1Solve a Rational Equation Example 2Elimination of a Possible Solution Example 3Work Problem Example 4Rate Problem Example 5Solve a Rational Inequality

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

  3. 6 1 1 1 1 1 Simplify. Simplify. Add. Example 6-1b

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

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

  6. Solve Answer: Example 6-1e

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

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

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

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

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

  12. Solve Answer: Example 6-2f

  13. In 1 hour, Tim could complete of the job. In 1 hour, Ashley could complete of the job. Example 6-3a Mowing Lawns Tim and Ashley mow lawns together. Tim working alone could complete the job in 4.5 hours, and Ashley could complete it alone in 3.7 hours. How long does it take to complete the job when they work together?

  14. In t hours, Tim could complete or of the job. In t hours, Ashley could complete or of the job. Part completedby Tim plus part completedby Ashley equals entire job. 1 Example 6-3b

  15. Original equation Multiply eachside by 16.65. DistributiveProperty Simplify. Example 6-3c Solve the equation.

  16. Simplify. Divide each side by 8.2. Example 6-3d Answer: It would take them about 2 hours working together.

  17. Example 6-3e Cleaning Libby and Nate clean together. Nate working alone could complete the job in 3 hours, and Libby could complete it alone in 5 hours. How long does it take to complete the job when they work together? Answer: about 2 hours

  18. Words The formula that relates distance, time, and rate is Example 6-4a Swimming Janine swims for 5 hours in a stream that has a current of 1 mile per hour. She leaves her dock and swims upstream for 2 miles and then back to her dock. What is her swimming speed in still water? Variables Let r be her speed in still water. Then her speed with the current is r + 1 and her speed against the current is r – 1.

  19. Time going withthe current plus time going againstthe current equals totaltime. 5 Equation Originalequation Example 6-4b Solve the equation.

  20. Multiply eachside by r2 – 1. r + 1 r – 1 DistributiveProperty 1 1 Simplify. Simplify. Subtract 4rfrom each side. Example 6-4c

  21. Quadratic Formula x = r, a = 5, b = –4, and c = –5 Simplify. Example 6-4d Use the Quadratic Formula to solve for r.

  22. Simplify. Use a calculator. Example 6-4e Answer: Since the speed must be positive, the answer is about 1.5 miles per hour.

  23. Example 6-4f Swimming Lynne swims for 1 hour in a stream that has a current of 2 miles per hour. She leaves her dock and swims upstream for 3 miles and then back to her dock. What is her swimming speed in still water? Answer: about 6.6 mph

  24. 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.

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

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

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

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

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

  30. Answer: The solution Example 6-5g

  31. Solve Answer: Example 6-5h

  32. End of Lesson 6

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