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Equations as Balances x 3 5 1 1 1 x 1 1 1 1 1 Take 3 away from each side 1 x 1 3] x2 The golden rule of solving equations Whatever you do to one side of the equation, you must do to the other. 1 The golden rule of solving equations x x 1 Whatever you do to one side of the equation, you must do to the other. This means that we have taken 1 away from each side. 1 2x 1 7 1 1 1 1 1 1 x x 1] 2x 6 1 1 1 x 2] 1 1 1 1 1 x 3 1 1 x x 1 x 1 1 1 1 2x 1 x 6 x] x 1 6 1] x 5 Solving Equations Showing Good Working x 5 12 5x 3 33 3] 5x 30 5] x6 5] 3 5 x x] 3 x 5 3] x2 x 17 5x 8 5] x 85 Equation To understand what comes later, let’s show it Reversing The Flow Chart to Solve the Equation as a Flow Chart x 4 7 x 3 8 x x 2x 6 40 x 4 3 2 7 4 x 28 7 8 3 x 5 8 2x 6 2 6 x 17 34 40 40 What it means 5x 4 8 x 3( x 4) 27 x x 4 5 3 x 5 4 4 5x 4 How we will solve 8 4 12 5 x 12 5 8 4 3 27 3 9 x4 27 x 4 5 3 x 5 5 2 4 x 8 3 Example 1 x x 1 1 x 1 1 1 1 2x 1 x 6 x] 1] 2x x 1 x x 6 x 1 6 x 1 1 6 1 x 5 Example x x x x x x 1 x 1 x 1 x 1 1 1 1 1 6x 1 3x 7 3x] 6x 3x 1 3x 3x 7 1] 3] 3x 1 1 7 1 3x 2 3 3 3x 1 7 3x 6 x2 More examples 7 x 6 4x 12 5x 3 2 x 5 2x] 3x 3 5 4x] 3x 6 12 3] 3x 2 6] 3x 18 3] x 3] x6 2 3 3x 1 5x 11 3x] 1 2x 11 11] 10 2x 2] 5 x