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16. 17. EOC Practice. 18. 19. EOC Practice Continues. Essential Question : How can the solution of an equation with variables on both sides be found?.

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  1. 16. 17. EOC Practice

  2. 18. 19. EOC Practice Continues

  3. Essential Question: How can the solution of an equation with variables on both sides be found? • You need to get the variables on one side of the equation. It does not matter which variable you move. Try to move the one that will keep your variable positive. 1) Solve 3x + 2 = 4x - 1 Steps to solving 2-step equations 1. Draw “the river” 2. Subtract 3x from both sides 3. Simplify 4. Add 1 to both sides 5. Simplify

  4. 2) Solve 8y - 9 = -3y + 2 What is my goal? Could I use any previously taught strategies to solve this equation? Can I combine like terms that are on opposite sides? If so, is there an additional strategy I must apply?

  5. What is the value of x if 3 - 4x = 18 + x? • -3 • 3

  6. 3) Solve 4 + 2x = 13x - 3x

  7. 4) Solve -7(x - 3) = -7

  8. What is the value of x if 3(x + 4) = 2(x - 1)? • -14 • -13 • 13 • 14

  9. 5) Two times a number plus three equals one half of the number plus 12. What is the number?

  10. Special Case #1 6) 2x + 5 = 2x - 3 This is never true! No solutions

  11. Special Case #2 7) 3(x + 1) - 5 = 3x - 2 This is always true! Infinite solutions or identity HINT: It looks exactly the same on both sides

  12. What is the value of x if -3 + 12x = 12x - 3? • 0 • 4 • No solutions • Infinite solutions

  13. Practice: • To solve equations with variables on both sides of the equal sign: • 1- Distribute. • 2- Combine like terms. • 3- Move all the variables to the same side. • 4- Solve the two step equation. • Subtract or add • Divide. • *Every step isn’t needed in every equation. • 3(d – 8) = 3d • 4(p + 3) = 36 • 2(w – 1) + 4 = 4(w + 1) • 6(2 – 2y) = 5(2y – 2) • 5(p + 3) + 9 = 3(9 – 2) + 6

  14. Word Problem Practice: Christine can buy a new snowboard for $136.50. She will still need to rent boots for $8.50 a day. She can rent a snowboard and boots for $18.25 a day. How many days would Christine need to rent both the snowboard and the boots to pay as much as she would if she buys the snowboard and rents only the boots for the season?

  15. Let d represent the number of days. 18.25d = 136.5 + 8.5d – 8.5d – 8.5d Subtract 8.5d from both sides. Simplify. 9.75d = 136.5 9.75 9.75 Divide both sides by 9.75. d = 14 Christine would need to rent both the snowboard and the boots for 14 days to pay as much as she would have if she had bought the snowboard and rented only the boots.

  16. More Word Problem Practice: A local telephone company charges $40 per month for services plus a fee of $0.10 a minute for long distance calls. Another company charges $75.00 a month for unlimited service. How many minutes does it take for a person who subscribes to the first plan to pay as much as a person who subscribes to the unlimited plan?

  17. Let m represent the number of minutes. 75= 40 + 0.10m – 40 – 40 Subtract 40 from both sides. Simplify. 35= 0.10m 0.10 0.10 Divide both sides by 0.10. 350 = m If you are going to use more than 350 minutes, it will be cheaper to subscribe to the unlimited plan.

  18. Challenge! What is the value of x if -8(x + 1) + 3(x - 2) = -3x + 2? • -8 • -2 • 2 • 8

  19. Additional Practice: • Page 105 - 108 (10, 12, 14, 18, 22, 23, 26, 43, 57)

  20. Wrap-up: • Summary • Remember to answer the Essential Question • Important Information: Assessment #2 – • Periods: 1, 3, 5 [10/8/12] • Periods: 2, 4, 8 [ 10/9/12] • HLA#7: Page 105 (1-5)

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