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Warm Up

y 15. Warm Up. Solve. 1. 3 x = 102 2. = 15 3. z – 100 = 21 4. 1.1 + 5 w = 98.6 5. What are complementary and supplementary angles?. x = 34. y = 225. z = 121. w = 19.5. Solving Multi-Step Equations. Friday, November 7, 2014. 33. 11 x. =. 11. 11.

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Warm Up

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  1. y 15 Warm Up Solve. 1.3x = 102 2. = 15 3.z – 100 = 21 4. 1.1 + 5w = 98.6 5. What are complementary and supplementary angles? x = 34 y = 225 z = 121 w = 19.5

  2. Solving Multi-Step Equations Friday, November 7, 2014

  3. 33 11x = 11 11 To solve a multi-step equation, you may have to simplify the equation first by combining like terms. Example 1: Solving Equations That Contain Like Terms Solve. 8x + 6 + 3x – 2 = 37 11x + 4 = 37 Combine like terms. – 4– 4Subtract 4 from both sides. 11x = 33 Divide both sides by 11. x = 3

  4. ? 8(3) + 6 + 3(3) – 2 = 37 ? 24 + 6 + 9 – 2 = 37 ? 37 = 37 Example 1 Continued Check 8x + 6 + 3x – 2 = 37 Substitute 3 for x. 

  5. 39 13x = 13 13 Example 2 Solve. 9x + 5 + 4x – 2 = 42 13x + 3 = 42 Combine like terms. – 3– 3Subtract 3 from both sides. 13x = 39 Divide both sides by 13. x = 3

  6. ? 9(3) + 5 + 4(3) – 2 = 42 ? 27 + 5 + 12 – 2 = 42 ? 42 = 42 Example 2Continued Check 9x + 5 + 4x – 2 = 42 Substitute 3 for x. 

  7. If an equation contains fractions, it may help to multiply both sides of the equation by the least common denominator (LCD) to clear the fractions before you isolate the variable.

  8. Remember! The least common denominator (LCD) is the smallest number that each of the denominators will divide into.

  9. 7 7 7 –3 –3 3 4 4 4 4 4 4 5n 5n 5n ( )( ) 4 4 4 4 + = 4 ( )( )( ) 4 + 4 = 4 Example 3: Solving Equations That Contain Fractions Solve. + = – Multiply both sides by 4 to clear fractions, and then solve. Distributive Property. 5n + 7 = –3

  10. –10 Divide both sides by 5 5 5n = 5 Example 3 Continued 5n + 7 = –3 – 7–7Subtract 7 from both sides. 5n = –10 n = –2

  11. 5 5 5 –1 1 –1 2 2 2 4 4 4 3n 3n 3n 4 4 4 Example 4 Solve. + = – Multiply both sides by 4 to clear fractions, and then solve. ( )( ) 4 + = 4 ( )( )( ) Distributive Property. 4 + 4 = 4 3n + 10 = –1

  12. –11 Divide both sides by 3. 3 3n = 3 Example 4 3n + 10 = –1 – 10–10Subtract 5 from both sides. 3n = –11 n =

  13. Example 4

  14. 9 16 25 2x 5 x 6x 33 8 8 8 7 21 21 x = 1 Lesson Quiz Solve. 1. 6x + 3x – x + 9 = 33 2. –9 = 5x + 21 + 3x 3. + = 5. Linda is paid double her normal hourly rate for each hour she works over 40 hours in a week. Last week she worked 52 hours and earned $544. What is her hourly rate? x = 3 x = –3.75 x = 28 4. – = $8.50

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