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Rearranging Equations

Rearranging Equations. Things to remember:. Don’t rush it. You must go through each stage of your method and not try to skip any. If you are making x the subject it means that you want to end up with x = and this is the only x in your answer.

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Rearranging Equations

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  1. Rearranging Equations

  2. Things to remember: • Don’t rush it. You must go through each stage of your method and not try to skip any. • If you are making x the subject it means that you want to end up with x = and this is the only x in your answer. • Whatever you do to one side of the equals sign you must do to the other.

  3. Rearrange the equation to make a the subject b = 5a + 21 b – 21 = 5a b – 21 = a This means we want to rearrange the equation so it says a = -21 -21 ÷5 ÷5 5 Our answer should say ... a = b – 21 5

  4. Rearrange the equation to make t the subject h = 13 + 7t h – 13 = 7t h – 13 = t This means we want to rearrange the equation so it says t = -13 -13 ÷7 ÷7 7 Our answer should say ... t = h – 13 7

  5. Exercise One Rearrange each equation to make s the subject • u = 11s + 3 • w = 8s + p • q = 3s + 4t • 7s + m + t = l • a = 3(s + 4) • 4 = g(s – 7) • 22 + 5s = g • r = q – 3s Hint: You need to expand the brackets first

  6. 11 8 Rearrange each equation to make s the subject • u = 11s + 3  s = u - 3 • w = 8s + p  s = w – p • q = 3s + 4t  s = q – 4t • 7s + m + t = l  s = l – m – t • a = 3(s + 4)  s = a – 12 = a - 4 • 4 = g(s – 7)  s = 4 + 7g = 4 + 7 • 22 + 5s = g  s = g - 22 • r = q – 3s  s = q - r 3 7 3 3 g g 5 3

  7. Rearrange the equation to make v the subject e = 3v + t 5e = 3v + t 5e – t = 3v 5e – t = v This means we want to rearrange the equation so it says v = 5 x5 x5 - t - t ÷3 ÷3 3 Our answer should say ... v = 5e – t 3

  8. Rearrange the equation to make p the subject m = p + n m - n = p 2(m – n) = p This means we want to rearrange the equation so it says p = 2 - n - n 2 x2 x2 Our answer should say ... p = 2(m – n)

  9. a = x + x = Examplemore difficult Rearrange the equation a = x + to make x the subject. Method - ad = dx + cx multiply both sides by d dx + cx = ad rearrange to get x’s on the left x(d + c) = ad factorise divide by (d + c)

  10. a = + p = Examplemore difficult Rearrange the equation a = + to make p the subject. Method - apq = q + p multiply both sides by pq apq – p = q rearrange to get p’s on the left p(aq – 1) = q factorise divide by (aq – 1)

  11. Examplemore difficult Rearrange the equation a = b + to make p the subject. Method - a = b + a(1 + p) = b(1 + p) + c multiply both sides by 1 + p a + ap = b + bp + c expand brackets ap – bp = b + c – a rearrange to get p’s on the left factorise p(a – b) = b + c – a divide by (a – b) p =

  12. Examplemore difficult Rearrange the equation s = b + to make t the subject. Method - s = b + s – b = subtract b from both sides (s – b)² = square both sides = (s – b)² rearrange to get t on the left multiply by p t = p(s – b)²

  13. Check your answers on previous slides Test Yourself 4. Rearrange the equation s = b + to make t the subject. 1. Rearrange the equation a = x + to make x the subject. 2. Rearrange the equation a = + to make p the subject. 3. Rearrange the equation a = b + to make p the subject.

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