Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
CANADIAN MATHEMATICS 8 6.3 SOLVING TYPE III EQUATIONS , A Type III equation is one where there is more than one group of variables (letters). To solve aType III equation you should first collect and place all the variables (letters) on the left side of the equal sign or equation, and all the constants (numbers) on the right side of the equal sign or equation by using opposite operations. That means if an 'x' term is on the right side of the equal sign, bring it over to the left side by using the opposite sign. Likewise, if a number is being added or subtracted on the left side of an equation, bring it over to the right side by using the opposite sign as shown in the two examples below. EXAMPLE #1 EXAMPLE #2 5x - 3 = 3x + 14 5x -3x = 14 + 3 2x = 17 2x = 17 2 2 x=8.5 6x - 4.3 + 3x = 86.2 - lx 6x + 3x + lx = 86.2 + 4.3 10x = 90,5 10x = 90.5 10 10 x = 9.05 A. Solve the following. 1. 3x + 8x = 44 2. 7x - 3x = 44 3. -2x - 8x = -100 4. 1/ 3 y + 2/ 3 y = 14 5. -3.2a + 5a = 90 6. 12 = 3/ 4 x + 5/ 4 x 7. 7x -5x ---- -20 8. 3x - 10x = 15 9. 4x + 3.2x= 18 10. 7x + 6 = 12 11. 5x - 3 = 2x + 8 .12. 14. 4x + 3 = 9x + 7 , 15. 1/ 2 x + 2 = 3/ 4 x + 7 16. 0.4x + 8 = 0.6x - 7 17. 6x + 1.2 = 9x + 2 18. 6/ x - 2 = 2/ 7 x + 8 19. + 20 = x + 4 20. 1/ 2 a + 9 = 2a - 6 21. 0.02x + 7 = 0.03x + 5 22. 5x - 10 = 25x + 3 23. 7x - 10 = 3x + 14 24. 0.1y + 0.01 = 0.01y + 0.1 25. 3x ± 10 + 5x = 90 26. 6 -5 -2x = 7 + 1 27. 16 ±45x = 39x + 310 28. 7x - 3 - 2x = 8 29. 8x + 4x + 5x = 7 71. ,R7A 4.0 13. -2/ 3 x+5=7 3X EQUATIONS AND INEQUALITIES -5x - = -2x + 8 30. 2x - 3 = 6x + 4x 75 CANADIAN MATHEMATICS 8 B. Extra Practice. Solve the following. 1. 3x + 6x = 81 2. 3x + 6 = 2x + 5 kir0/ 4. 617 x - 2 = 2/ 7 x + 8 5. 6x + 1.2 = 9x + 2 7. 64 = -3x - 5x 3. 32 + 90x = 78x + 620 8. 5x - 3 = 2x + 8 6. 2x + 5 - 3x + 8 = 7 9. 6x + bx + 360 = 600 10. 12 - 8y = 5y - 14 11. -3x + 7 = 3x - 17 12. x + 3 + x + 8 = 22 13. 5x = 4x 14. 12x + 13x = 50 15. -3x + 2x - 6x = 49 16. -5x•- = -2x + 8 17. 4x + 3 = 9x + 7 18. 3x - 8 = 7x + 5 19. 8x - 9 = 25 - 20. x + 2x + 3x = 30 21. x + x + 4 + x + 8 = 96 22. 60 + 3x = 200 - 2x 23. 5x - 3 = 2x + 8 . 24. 1/ 2 X + 2 = 3/ 4 x - 7 25. 4x = 3x + 2x - 5 26. 3x - x = 16 27. 9y + 45 = -ly + 135 28. 4x - x + 7x = 15 29. 7x - 8= 3x + 5 30. 0.4x + 8 = 0.6x - 8 31. 0.3x - 4 = 0.6x - 8 32. 3x = 5x + 6 33. 5x + 100 - 2.5x = 165 34. 0.5x + 9 = 2x - 6 35. 1/ 3 x + 20 = x + 4 36. 7.2x + 9 = 5.2x - 8 37. 7x + 8 = 6x 38. 2x - 8 = 3x + 5 39. 0.3x + 1.6 = 0.4x + 1.9 40. 5x + 3 = 4x + 3 41. 7x - 42. 1/ 2 X - 8 = 1/ 4 X + 3 = 67 + 33 43. 8x + 3x + 5x = -256 44. 1/ 2 X+ / 3 x = 12 46. 14x + 12 = 24 47. 9x -30x = 45 _ 45 4x = 12x + 8x 48. 14x -6x -4x = 16 va; {.76 I CHAPTER CANADIAN MATHEMATICS 8 6.3 SOLVING TYPE III EQUATIONS A Type III equation is one where there is more than one group of variables (letters). To solve a TypOI equation you should first collect and place all the variables (letters) on the left side of the equal lign or equation, and all the constants (numbers) on the right side of the equal sign or equation by using opposite operations. That means if an 'x' term is on the right side of the equal sign, bring it over to the left side by using the opposite sign. Likewise, if a number is being added or subtracted on the left side of an equation, bring it over to the right side by using the opposite sign as shown in the two examples below. EXAMPLE #2 EXAMPLE #1 6x - 4.3 + 3x = 86.2 - lx 6x + 3x + lx = 86.2 + 4.3 10x = 90.5 10x = 90.5 10 10 x =9.05 . 5x - 3 = 3x + 14 5x -3x = 14 + 3 2x = 17 2x = 17 2 2 x 8.5 A. Solve the following. 1. 3x + 8x = 44 j1 Li 3 y + 2/ 3 y = 14 10. 7x + 6 = 12 c. -3 (c) 8. 3x - 10x = 15 _L 11. 5x - 3 = 2x + 8 c2.5 12. -5x - 3 = -2x + 8 3I 14. 4x + 3 = 9x + 7 . - -3 _2315. 1/ 2 x + 2 = 3/ 4 x + 7 -a0 5" - 0 . a to 19. 1/ 3 x + 20 = x + 4 ;1/49 20. 1/ 2 a + 9 = 2a - 6 22. 5x -10 = 25x + 3 23. 7x -10 = 3x +14 -13 9. 4x + 3.2x = 18 - a -) 16. 0.4x + 8 = 0.6x - 7 17. 6x + 1.2 = 9x± 2 -75 6. 12 = 3/ 4 x + 5/ 4 x 5D --:1 13. -2/ 3 x + 5 = 7 -10 5. -3.2a + 5a = 90 / Li 7. 7x - 5x = -20 . -ID 3. -2x - 8x = -100 2. 7x - 3x = 44 /0 6 18. -2 = 2/ 7 x + 8 /7 -5 21. 0.02x + 7 = 0.03x + 5 aD 0 24. 0.1y + 0.01 = 0.01y + 0.1 i .a.c. 25. 3x +•10 + 5x = 90 10 26. 6x -5 -2x = 7 + 1 27. 16 + 45x = 39x -i- 310 28. 7x - 3 - 2x = 8 29. 8x + 4x.+ 5x =7 3-a5" -7 EQUATIONS AND INEQUALITIES 30. 2x -3 = 6x + 4x 4 CANADIAN MATHEMATICS 8 4 4 4 B. Extra Practice. Solve the following. 1. 3x + 6x = 81 2. 3x + 6 = 2x + 5 , Li -I , 3. 32 + 90x = 78x + 620 4. 617 x - 2 = 2/ 7 x + 8 5. 6x + 1.2 = 9x + 2 6. 2x + 5 - 3x + 8 = 7 17.5 7. 64 = -3x -5x 8. 5x -3 = 2x + 8 ‘, 4 4 4 9. 6x + 6x + 360 = 600 10. 12 - 8y = 5y - 14 11. -3x + 7 = 3x - 17 a 5.6 14. 12x + 13x = 50 13. 5x = 4x 0 12. x + 3 + x + 8 = 22 ,. a 15. -3x + 2x - bx = 49 -i 16. -5x - 3 = -2x + 8 17. 4x + 3 = 9x + 7 18. 3x - 8 = 7x + 5 19. 8x - 9 = 25 - 9x 20. x + 2x + 3x = 30 21. x + x + 4 + x + 8 = 96 22. 60 + 3x.= 200 - 2x 23. 5x - 3 = 2x + 8 25. 4x = 3x + 2x -5 26. 3x - x = 16 _.1._ - 3 if 24. "2 X + 2 = 3/ 4 x - 7 3( 27. 9y + 45 = -1y + 135 1 5 28. 4x - x + 7x = 15 29. 7x - 8 = 3x + 5 30. 0.4x + 8 = 0.6x - 8 31. 0.3x - 4 = 0.6x - 8 32. 3x = 5x + 6 33. 5x + 100 - 2.5x = 165 /3:11 -3 35. 1/ 3 x + 2,0 = x + 4 36. 7.2x + 9 = 5.2x - 8 37. 7x + 8 = 6x 38. 2x - 8 = 3x + 5 39. 0.3x + 1.6 = 0.4x+ 1.9 40. 5x + 3 = 4x + 3 0 -13 41. 7x - 5x = 67 + 33 50 43. 8x + 3x + 5x = -256 44. 1/ 2 x +/ 3 x = 12 -16 46. 14x + 12 = 24 6 ---- /1.14 47. 9x - 30x = 45 1 - / 4 4 4 4 4 ca6 34. 0.5x + 9 = 2x - 6 / 0 -8 4 4 4 4 4 4 -3 42. 112 x - 8 = 1/ 4 x + 3 44 45. 4x -6 = 12x + 8x __ 3 ? 48 14x - 6x - 4x = 16 LI CHAPTER 6 4 4