3 2 Solving Linear Equations

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3 2 Solving Linear Equations

  1. 1. To solve an equation is to isolate the variable.
  2. 2. To isolate the variable means to get it alone on one side of the equation.
  3. 3. Given the equation,how do we isolate the x? x =4 7
  4. 4. What number has to move to leave x alone on one side of the equation? x =4 7
  5. 5. What number has to move to leave x alone on one side of the equation? x =4 7
  6. 6. If we couldmove the seven, x =4 7
  7. 7. If we could move the seven,the x would be isolated. x =4 77 77 77 77
  8. 8. The next question is,how can we move the 7? x =4 7
  9. 9. What is the sevendoing in the equation? x =4 7
  10. 10. What operationundoes division? x =4 7
  11. 11. To move the 7, we just need to multiplyboth sides of the equation by 7. x =4 7
  12. 12. Remember . . . when you do somethingto one side of an equation x 7 ⋅ =4 7
  13. 13. you have to do exactly the same thing to the other side. x 7 ⋅ =4 ⋅ 7 7
  14. 14. When we simplify, x 7 ⋅ =4 ⋅ 7 7
  15. 15. When we simplify,we will have our solution. x = 28
  16. 16. To solve equationsthat involve multiplication you divide, 3a = 15 3 3
  17. 17. To solve equationsthat involve multiplication you divide, a=5
  18. 18. and to solve equations that involve division you multiply. b 9 ⋅ = −2 ⋅ 9 9
  19. 19. and to solve equations that involve division you multiply. b = −18
  20. 20. When Val works at the zoo on Saturday, she earns $10.80 perhour. She also is paid $8 for meals and $3 for transportation.Last Saturday she received $83.90. How many hours did shework??Ms. Toshio bought gas for $2.39 per gallon and a drink for$1.50. The total bill was $31.15 before sales tax. How manygallons of gas did she buy??Bena lives in Delaware, where there is no sales or meals tax.She bought three chicken sandwiches with a $10 bill andreceived $1.45 change. What was the price of one sandwich??

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