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Equation Rearrangement Examples and Solutions

Learn how to rearrange equations and find gradients with step-by-step examples and explanations.

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Equation Rearrangement Examples and Solutions

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  1. 2 1. Rearrange the equation 2p + 1 = 11 to make p the subject. what has happened top? inverse 2 = 11 p + 1 - 1

  2. u 2. Rearrange the equation uv + f = t to make v the subject. what has happened tov? inverse u = t v + f - f

  3. 3. Line L1 has equation y– 4x = 9, by rearranging the equation write down the gradient of the line L1 Wrong answers There is a temptation to say that the gradient is -4 (as this is what is multiplying x) or -4x = 11 y - 4x + 4x Gradient We have rearranged the equation of the line from y– 4x = 9 toy = 9 + 4x , the gradient is therefore + 4 (as this is what is multiplying x)

  4. 4. Line L2 has equation y– 6x = 12, by rearranging the equation write down the gradient of the line L2 Wrong answers There is a temptation to say that the gradient is -6 (as this is what is multiplying x) or -6x = 12 y - 6x + 6x Gradient We have rearranged the equation of the line from y– 6x = 12 toy = 12 + 6x , the gradient is therefore + 6 (as this is what is multiplying x)

  5. 2 5 (b) By rearranging the equation 2y – 6x = 12 to make y the subject write down the gradient of the line 2y – 6x = 12 There is a temptation to say that the gradient is -6 (as this is what is multiplying x), -6x or + 6 (taking -6x across the equals). Wrong answers 2 = 12 y - 6x + 6x Gradient If we divide the top of the fraction by two we get: y = 6 + 3x The gradient of the line is 3, as this is multiplying x.

  6. 5 (c) A student looks at the equation 2y – 6x = 12and writes down the y-intercept as equal to 12. Explain whether the student is correct or not. rearranged equation y = 6 + 3x general equation y = m x + c gradient y-intercept 6 =

  7. Will have to press more than once 6. Multiply out the brackets and collect like terms x x 1 2 x2 2 x 1 5 x 5 x 5 2 x 10 Collect like terms 25

  8. Will have to press more than once 6. Multiply out the brackets and collect like terms + + + Collect like terms + +

  9. Will have to press more than once 6. Multiply out the brackets and collect like terms x x 2 3 x2 6 x 2 4 x 8 x 3 3 x 9 Collect like terms 12

  10. Will have to press more than once 6. Multiply out the brackets and collect like terms + + + Collect like terms + +

  11. Will have to press more than once 6. Multiply out the brackets and collect like terms x x 3 2 x2 6 x 3 -1 x -3 x 1 2 x 2 Collect like terms -1

  12. Will have to press more than once 6. Multiply out the brackets and collect like terms + + + Collect like terms + +

  13. Will have to press more than once 6. Multiply out the brackets and collect like terms x x 1 1 x2 1 x 1 -1 x -1 x 2 1 x 2 Collect like terms -2

  14. Will have to press more than once 6. Multiply out the brackets and collect like terms + + + Collect like terms + +

  15. Will have to press more than once 6. Multiply out the brackets and collect like terms x x 1 1 x2 1 x 1 y xy 1 x y 1 xy 1 Collect like terms y2

  16. Will have to press more than once 6. Multiply out the brackets and collect like terms + + + Collect like terms + +

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