2. BALANCING EQUATIONS We can think of an equation like a set of scales with two sides that balance. That means that you can change one side if you do the same to the other so that it remains balanced.

3. Example 1 Solve this balancing equation: 3 tins + 15 kg = 6 tins 15 kg= 3 tins(Taking 3 tins from both sides) 3 tins = 15 kg 1 tin = 5 kg + 15 kg =

4. Example 2 Form a balancing equation and solve it. 4 t + 20 = 6 t 20 = 2t (Taking 4 tins from both sides) 2t = 20 t = 10 + 20 =

5. 4 t + 30 = 10 t 30 = 6t(Taking 4t from both sides) 6 t = 30 1 t = 5 Example 3 Draw your own picture if you need it. More Practice 8 t = 3 t + 350 5t + 4 = 34 12 t + 14 = 62

6. Equations with brackets 1 4(2t + 3) = 44 8t + 12 = 44 (Multiplying out bracket) 8t = 32 (Subtracting 12 from both sides) t = 4 (Dividing by 8)

7. Equations with brackets 2 5(8t - 4) = 220 40t - 20 = 220 (Multiplying out bracket) 40t – 20 ( +20) = 220 ( +20) ( add 20 to both sides) 40t = 240 (Dividing by 40) t = 6

8. 5(5t + 3) = 165 25t + 15 = 165 25t = 150 t = 6

9. 7(9t - 3) = 294

10. 2(8t - 10) = 44

11. 2(5t - 3) = 8t

12. 3(5t - 8) = 3t

13. Tins and kg on both sides 3t + 15 = 6t + 3 15 = 3t + 3 (Taking 3t from both sides) 12 = 3t (Taking 3 from both sides) t = 4 + 15 kg = + 3kg

14. 5t + 4 = 2 t + 10 (Taking 2t from both sides) 3t + 4 = 10 (Taking 4 from both sides) 3 t = 6 t = 2 + 4 kg = + 10 kg Form your own equation from the picture and solve it.

15. 1.Take as many of the letter as you can from both sides. 2.Take as many numbers as you can from both sides. 3.You should be left with letters on one side and numbers on the other side. 4.Divide to find what the letter equals. 5.Check by substituting back in to the equation. The left should equal the right hand side.

16. 6t + 8 = 2t + 12 4t + 8 = 12 (Taking 2t from both sides) 4t = 4 (Taking 8 from both sides) t = 1 More Practice 6t + 51 = 13t + 30 7t + 9 = 4t + 24 5t + 24 = 12t + 10 2(5g + 3) = 6(g + 5)

17. 6t + 51 = 13t + 30 51 = 7t + 30 (Taking 6t from both sides) 21 = 7t (Taking 30 from both sides) t = 3

18. 7t + 9 = 4t + 24 3t + 9 = 24 3t = 15 t = 5

19. 5t + 24 = 12t + 10 24 = 7t + 10 (Taking 5t from both sides) 14 = 7t (Taking 10 from both sides) t = 2

20. Forming expressions and solving equations 1.Write an expression for the perimeter of this rectangle using brackets. 3x + 5 2x + 6 2.The perimeter is 38 cm. Write an equation. 3.Solve your equation. 4.Work out the length and width of the rectangle.

21. Forming expressions and solving equations 2 1.Write an expression for the perimeter of this rectangle. 4b + 7 b + 4 2.The perimeter is 62 cm. Write an equation. 3.Solve your equation. 4.Work out the length and width of the rectangle.

22. Forming expressions and solving equations 3 1.Write an expression for the perimeter of this rectangle. a + 8 2a + 5 2.The perimeter is 4a + 36 cm. Write an equation. 3.Solve your equation. 4.Work out the length and width of the rectangle.