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GCSE Maths Creating equivalent equations Task 1 Complete these stages. Look at these stages of separation. x=4 ? x+1=5 ? 4x + 1 = 3x + 5 What has been done at each stage to the equation? Does each equation have the same root (solution)? Task 2 Complete these stages. x=4 Subtract 1 2(x – 1) = 6 Complete the box and empty ‘bubble’. The first equation is known as the root equation, or just root. Does each of these equations have the same root? We are trying to create groups of equations with the same root equation. Task 3 Complete these stages. x=4 x=4 Double Subtract 5 ? 2x + 1 = 9 Activity 1 How many equations can you create with roots x=5 x=3 x = -2 ? Activity 2 What happens when you multiply both sides by x? Divide by two Activity 3 What happens when you square both sides? Activity 4 Take some of your stages and write them backwards. Explain the processes and how they compare to the original sequence. Activity 5 Write down the rules you have discovered that work for equations.