3. x + 5 = 20

4. x+5 20 (-5) x + 5 = 20

5. x 20 (-5) x + 5 = 20

6. x 15 x = 15 x + 5 = 20

7. (-5) (-5) x = 15 Example 1: x + 5 = 20

8. 1)x + 8 = 122) a + 12 = 30 3)5 + x = 134)b + 7 = 42 (-8) x = 4 (-12) a = 18 (-5) x = 8 (-7) (-7) b = 35 Answers Exercise 1

9. 3x + 7 = 25

10. 3x+7 25 (-7) 3x + 7 = 25

11. 3x 25 3x + 7 = 25 (-7)

12. 3x 18 3x = 18 3x + 7 = 25 ?

13. This means 3 times x equals 18 3 times 6 equals 18 So x must be 6 x = 6 3x = 18

14. 3x + 7 = 25 (-7) (-7) 3x = 18 Example 2: x = 6

15. 1) 2x + 7 = 23 2) 6a + 11 = 29 3) 5 +8y = 37 4) 9 + 3d = 42 (-7) (-7) 2x = 16 x = 8 (-11) (-11) 6a = 18 a = 3 (-5) (-5) 8y = 32 y = 4 (-9) (-9) 3d = 33 d = 11 Exercise 2 Answers

16. 5x - 6 = 44

17. 5x-6 44 (+6) 5x - 6 = 44

18. 5x 44 5x - 6 = 44 (+6)

19. 5x 50 5x = 50 5x - 6 = 44

20. (+6) (+6) 5x = 50 Example 3: x = 10

21. 1) 5b - 8 = 122) 7a - 9 = 33 3) 6y - 6 = 304) 9z- 7 = 20 (+8) (+8) 5b = 20 b = 4 (+9) (+9) 7a = 42 a = 6 (+6) (+6) 6y = 36 y = 6 (+7) (+7) 9z = 27 z = 3 Exercise 3 Answers

22. Is there a shortcut?

23. 5x - 6 = 44 Change side, change sign - 6

24. 5x = 44 + 6 5x = 50 x = 10 Change side, change sign

25. 5x - 6 = 44 5x = 44+6 5x = 50 Example 4: x = 10

26. 3x + 7 = 25 Change side, change sign

27. 3x = 25 - 7 3x = 18 x = 6 Change side, change sign

28. 3x + 7 = 25 3x = 25 - 7 3x = 18 Example 5: x = 6

29. 1) 2a + 7 = 23 2) 7x - 9 = 33 2a = 23 - 7 2a = 16 a = 8 7x = 33 + 9 7x = 42 x = 6 Exercise 4 Answers

30. 5x + 2 = 3x + 6

31. 5x+2 3x+6 (-2) 5x + 2 = 3x + 6

32. 5x (-2) 3x+6

33. 5x 3x+4 (-3x) 5x + 2 = 3x + 6

34. 5x 4 (-3x)

35. 2x 4 2x = 4 5x + 2 = 3x + 6 So x = 2

36. Change side, change sign 5x = 3x + 6 - 2 5x = 3x + 43x 5x –3x = 4 2x = 4 5x + 2 = 3x + 6 x = 2 + 2

37. Change side, change sign 3x + 6 + 4 = 8x 3x + 10 = 8x3x 10 = 8x – 3x 10 = 5x 3x + 6 = 8x - 4 x = 2 - 4 Most Xs are on the right. So this time: Xs on the right, numbers on the left! 3x 8x

38. 3x + 6 = 8x - 4 6+4 = 8x – 3x Example 6: 10 = 5x x = 2 Try two changes together!

39. 1) 5a + 7 = 2a + 22 2) 3x + 9 = 7x - 15 5a – 2a = 22 - 7 3a = 15 a = 5 9 + 15 = 7x – 3x 24 = 4x x = 6 Exercise 5 Answers