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# OCR GCSE Maths Linear equations

To find the unknown in a linear equation the balancing method can be used. In the balancing method we either add or subtract the same value on each side of the equation so that only the unknown is left on one side of the equal sign.

To solve a linear equation that contains a set of brackets first use the balance method so that the brackets are alone on one side of the equation. Next divide the whole equation by the value in front of the brackets and then use the balance method to solve the rest of the equation.

To prove that two expressions are equivalent use the method to solve linear equations on both expressions and show that they have the same solution.

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Solve 7x β 2 = β9.

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Let x = 3. Which of the following equations does x not solve?

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Solve 3(w + 2) = 21 for w.

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Solve β4(x β 4) = 7.

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Solve 2(3 β x) + 4 = 4x β 2.

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Prove that β4x + 5 = 9 and 2x + 5 = 3 are equivalent.

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Are the expressions 3x + 1 = 16 and 4x β 1 = 11 equivalent? If so, prove this.

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Which of the following equations are equivalent?
A) 2(x + 1) = 4
B) 3x + 4 = 1
C) β3(x + 2) + 2 = β1

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