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What went wrong!

What went wrong!. -8k = -56 -8 -8 k = 7 Their Answer : k= -7. What went wrong!. 180k = 2 180 180 k = Their Answer : k= 90. What went wrong!. -2 – 3m = 1 +2 = +2 -3m = 3 -3 -3 m = -1 Their Answer : m = 0. What went wrong!. 2x + 4 = 4

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What went wrong!

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  1. What went wrong! -8k = -56 -8 -8 k = 7 Their Answer: k= -7

  2. What went wrong! 180k = 2 180 180 k = Their Answer: k= 90

  3. What went wrong! -2 – 3m = 1 +2 = +2 -3m = 3 -3 -3 m = -1 Their Answer: m = 0

  4. What went wrong! 2x + 4 = 4 -4 = -4 2x = 0 x = 0 Their Answer: x = 2

  5. What went wrong! -4 – g = -2 +4 = +4 -g = 2 g = -2 Their Answer: g = 2

  6. Warm Up Simplify. 1. 4x – 10x 2. –7(x – 3) 3. 4. 15 – (x – 2) Solve. 5. 3x + 2 = 8 6. –6x –7x + 21 2x + 3 17 – x 2 28

  7. Helpful Hint Equations are often easier to solve when the variable has a positive coefficient. Keep this in mind when deciding on which side to "collect" variable terms. To solve an equation with variables on both sides, use inverse operations to "collect" variable terms on one side of the equation.

  8. –5n = –5n + 2 =+ 2 Example 1: Solving Equations with Variables on Both Sides Solve 7n – 2 = 5n + 6. 7n – 2 = 5n + 6 To collect the variable terms on one side, subtract 5n from both sides. 2n – 2 = 6 2n = 8 Since n is multiplied by 2, divide both sides by 2 to undo the multiplication. n = 4

  9. –3b = –3b – 2 = – 2 Check It Out! Example 1a Solve 4b + 2 = 3b. 4b + 2 = 3b To collect the variable terms on one side, subtract 3b from both sides. b + 2 = 0 b = –2

  10. To solve more complicated equations, you may need to first simplify by using the Distributive Property or combining like terms.

  11. +36 = +36 + 2a = +2a Example 2: Simplifying Each Side BeforeSolving Equations Solve 4 – 6a + 4a = –1 – 5(7 – 2a). Distribute –5 to the expression in parentheses. 4 – 6a + 4a = –1 –5(7 – 2a) 4 – 6a + 4a = –1 –5(7) –5(–2a) 4 – 6a + 4a = –1 – 35 + 10a Combine like terms. 4 – 2a = –36 + 10a Since –36 is added to 10a, add 36 to both sides. 40 – 2a = 10a To collect the variable terms on one side, add 2a to both sides. 40 = 12a

  12. Example 2 Continued Solve 4 – 6a + 4a = –1 – 5(7 – 2a). 40 = 12a Since a is multiplied by 12, divide both sides by 12.

  13. Distribute to the expression in parentheses. 1 2 To collect the variable terms on one side, subtract b from both sides. 1 2 + 1 + 1 Check It Out! Example 2A Solve . 3 = b – 1 Since 1 is subtracted from b, add 1 to both sides. 4 = b

  14. –2x –2x – 6 – 6 Check It Out! Example 2B Solve 3x + 15 – 9 = 2(x + 2). Distribute 2 to the expression in parentheses. 3x + 15 – 9 = 2(x + 2) 3x + 15 – 9 = 2(x) + 2(2) 3x + 15 – 9 = 2x + 4 3x + 6 = 2x + 4 Combine like terms. To collect the variable terms on one side, subtract 2x from both sides. x + 6= 4 Since 6 is added to x, subtract 6 from both sides to undo the addition. x = –2

  15. Example 4: Application Jon and Sara are planting tulip bulbs. Jon has planted 60 bulbs and is planting at a rate of 44 bulbs per hour. Sara has planted 96 bulbs and is planting at a rate of 32 bulbs per hour. In how many hours will Jon and Sara have planted the same number of bulbs? How many bulbs will that be?

  16. 32 bulbs each hour 44 bulbs each hour the same as 60 bulbs 96 bulbs ? When is plus plus Example 4: Application Continued Let hrepresent the number of hours, and write expressions for the number of bulbs planted. 60 + 44h= 96 + 32h 60 + 44h= 96 + 32h To collect the variable terms on one side, subtract 32h from both sides. – 32h= – 32h 60 + 12h= 96

  17. Example 4: Application Continued 60 + 12h= 96 Since 60 is added to 12h, subtract 60 from both sides. –60 =– 60 12h= 36 Since h is multiplied by 12, divide both sides by 12 to undo the multiplication. h= 3

  18. Example 4: Application Continued After 3 hours, Jon and Sara will have planted the same number of bulbs. To find how many bulbs they will have planted in 3 hours, evaluate either expression for h = 3: 60 + 44h= 60 + 44(3) = 60 + 132 = 192 96 + 32h= 96 + 32(3) = 96 + 96 = 192 After 3 hours, Jon and Sara will each have planted 192 bulbs.

  19. If $299 is 30% off, then it must be 70% of the original price Let x be the original price After being discounted 30%, a TV sold for $299. What was the original price? Equation:___________ Solution:___________ Divide both sides by .7 to undo the multiplication

  20. Let c be the cost to make a dozen cookies You sell your homemade cookies for $6 a dozen. This is with a 25% mark-up. How much did it cost you to make the cookies? Mark-up means profit. A 25% profit means I covered my cost and earned 25% of the original cost. So the selling price is 125% of the cost Equation:___________ Solution:___________

  21. 6x - 4 The perimeter of the following triangle is 81 units. Solve for x. 4x +1 2x Equation:___________ Solution:___________

  22. The perimeter of the following rectangle is 136 units. Find the length and width of the rectangle if the length is 6 more than twice the width. The perimeter is twice the length plus the width. So add the length and width, then multiply by two Distribute the 2 2w + 6 Equation:___________ Solution:___________ Don’t forget to find the length too!! w

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