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Warmups

Warmups. 1. What is the supplement of 56 °? What is the complement of (3x) °? Find three consecutive even integers whose sum is 54. 3-5 SOLVING EQUATIONS WITH THE VARIABLE ON BOTH SIDES.

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Warmups

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  1. Warmups • 1. What is the supplement of 56°? • What is the complement of (3x)°? • Find three consecutive even integers whose sum is 54.

  2. 3-5 SOLVING EQUATIONS WITH THE VARIABLE ON BOTH SIDES Objective: To solve equations with the variable on both sides, and to use the distributive property to solve equations.

  3. EXAMPLE 1 3x + 2 = 2x – 1 -2x -2x x + 2 = -1 - 2 - 2 x = -3 Check! 3(-3) + 2 = 2(-3) – 1 -9 + 2 = -6 – 1 -7 = -7 If variables are on different sides, you can NOT combine them! Must add/subtract to the other side. Always move the smaller coefficient.

  4. Example 2 5x + 2 = 5 – x + x + x 6x + 2 = 5 - 2 - 2 6x = 3 6 6 x = 1/2 • Check! 5(1/2) + 2 = 5 – 1/2 2.5 + 2 = 5 – 0.5 4.5 = 4.5

  5. TOO with a partner 1) 4x + 6 = 2x – 8 Answers: 1) x = -7 2) 7 – 3x = 10 – 4x 2) x = 3

  6. Special Cases 7 – 3x = x – 8 – 4x 7 – 3x = -8 – 3x + 3x + 3x 7 = -8 False! Answer: No Solution -6n + 15 = 15 – 6n + 6n + 6n 15 = 15 True! Answer: All Numbers

  7. Distributive Property Example 1 3(x + 2) = 18 3x + 6 = 18 - 6 - 6 3x = 12 3 3 x = 4 Check! 3(4 + 2) = 18 PEMDAS! 3(6) = 18 18 = 18

  8. Examples 2) 4(x – 3) = 24 Answers: 2) x = 9 3) -2(5 + x) = 3 3) x = -13/2

  9. TOO with a partner 4 – (x + 3) = 10 2x + 3(2 – x) = 10 4 – 3(x + 7) = 30 Answers: x = -9 x = -4 x = -47/3

  10. EXAMPLE 4 2(x – 3) + 5 = 3(x – 1) 2x – 6 + 5 = 3x – 3 2x – 1 = 3x – 3 - 2x -2x -1 = x – 3 +3 + 3 2 = x x = 2 Steps Distribute Combine Like Terms Move Variables Add/Subtract Multiply/Divide Final Answer: x = #

  11. Too For Homework • 2 + 6x – 3 = 8x + 4 – 2x • -10x + 5 + 2x = 6 – 4x – 1 • 12x + 5 = 10 + 14x – 5 – 2x Two are special cases One is normal Steps • Combine Like Terms • Move Variables • Add/Subtract • Multiply/Divide

  12. Homework • Worksheet #23

  13. Math Lab Warmups • The sum of three consecutive integers is 54. Find the three numbers. 2. The sum of 2 consecutive even integers is 114. Find the two numbers. 3. The sum of four consecutive even integers is 228. Find the four numbers.

  14. Agenda • Finish Bingo • Homework Time 

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