1. Introduction To Equation Solving. xx 2x + 1 = 4 Solve :

2. Solving A Basic Equation. Consider the equation below: x + 2 = 5 This can be represented by the scales and marbles below. The problem is to find out how many marbles are in the box to make the scales balance. x Remove two marbles from each side. (-2) x=3 The solution to the equation is x = 3. That is to say that there are three marbles inside the box to keep the scales balanced.

3. Further Example. Solve the equation : m + 4 = 7 Draw scales to represent the equation: m How many marbles can we remove from both sides? 4 marbles (-4) m =3 There are three marbles in the box to keep the scales balanced. Hence : m = 3

4. What Goes In The Box ? Solve the following equations: (1) x + 8 = 14 (2) t + 10 = 18 (3) w + 3 = 12 (4) h + 7 = 20 (5) f + 14 = 34 (6) b + 13 = 32 (7) g + 70 = 110 (8) s + 27 = 74 x = 6 t = 8 w = 9 h = 13 f = 20 b = 19 g = 40 s = 47

5. More Than One Box. Solve the equation: 3x = 9 Draw scales to represent the equation: xxx (1) If there are 9 marbles in three boxes how many are in 1 box ? 3 marbles  3 x=3 There are three marbles in each box.

6. What Goes In The Box ? 2 Solve the following equations: (1) 2f = 10 (2) 3m = 12 (3) 4t = 12 (4) 6k = 24 (5) 5y = 45 (6) 9 d = 54 f = 5 m = 4 t = 3 k = 4 y = 9 d = 6

7. Further Example. Solve the equation: 2x + 4 = 12 Draw scales to represent the equation. How many marbles can be removed from both sides? 4 marbles (-4) 2x=8 If two boxes contain 8 marbles how many marbles are in one box? 4 marbles  2 x=4 There are 4 marbles in each box. Hence x = 4 is the solution. xx

8. Solve the equation : 3x + 5 = 17 Draw scales to represent the equation: xxx How many marbles can you remove from both sides? 5 marbles. (-5) 3x=12 If three boxes contain 12 marbles then how many marbles are in one box ? 4 marbles  3 x=4 As there are 4 marbles in each box the solution is x = 4

9. What Goes In The Box ? 3 (1) 2h + 6 = 20 (2) 3n + 11 = 26 (3) 4w + 5 = 29 (4) 7t + 3 = 31 (5) 4r + 14 = 26 (6) 8f + 21 = 37 (7) 6a + 32 = 44 (8) 9p + 32 = 59 h = 7 n = 5 w = 6 t = 4 r = 3 f = 2 a = 2 p = 3 Solve the equations below:

10. Solving Equations With Subtractions. Solve the equation: 2y – 3 = 7 Draw scales to represent the equation: yy The take away three means that three marbles have fallen out of a box. If you place the three fallen marbles back in the box what must you do to the other side of the balance ? Add three marbles. +3 2y = 10 Now solve as before.  2 y = 5 There are 5 marbles in each box. y = 5

11. Further Example. Solve the equation: 3m – 7 = 11 Draw scales to represent the equation: mmm How many marbles must be added to each side? 7 marbles. +7 3m=18  3 m = 6 There are 6 marbles in each box. m = 6 Now solve as before.

12. What Goes In The Box ? 4. (1) 3n – 5 = 1 (2) 4f – 8 = 12 (3) 5h – 17 = 13 (4) 2k – 21 = 31 (5) 6d – 7 = 11 (6) 7r – 14 = 21 (7) 8v – 21 = 35 (8) 9p – 26 = 28 n = 2 f = 5 h = 6 k = 26 d = 3 r = 5 v = 7 p = 6 Solve the equations below:

13. More Complex Equations. Solve the equation: 4m – 2 = m + 7 Draw scales to show the equation: mmmmm How many marbles can you put back ? 2 marbles. (+2) 4m= m +9 How many boxes can you remove ? 1 box. (- m) 3m=9  3 m=3 There are three marbles in each box.

14. Further Example. Solve the equation: 6g – 3 = 2g + 9 Draw scales to show the equation: gggggggg How many marbles can we add to both sides ? 3 marbles. +3 6g=2g+12 How many boxes can you remove from both sides? 2 boxes (-2g) 4g=12  4 g=3 There are 3 marbles in each box.

15. What Goes In The Box 5 ? (1) 4 m – 3 = m + 15 (2) 6y – 2 = 2y + 18 (3) 6t + 3 = 3t + 15 (4) 8r – 7 = 3r + 23 (5) 10 w – 9 = 3w + 33 (6) 9f + 14 = 3f + 56 m = 6 y = 5 t = 4 r = 6 w = 6 f = 7 Solve the equations below :