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**Rearranging Equations**

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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.

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**This means we want to rearrange the equation so it says**

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 = ÷5 ÷5 5 Our answer should say ... a = b – 21 5

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**This means we want to rearrange the equation so it says**

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

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**Hint: You need to expand the brackets first**

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

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**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 11 8 3 7 3 3 g g 5 3

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**This means we want to rearrange the equation so it says**

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 x x5 - t t ÷ ÷3 3 Our answer should say ... v = 5e – t 3

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**This means we want to rearrange the equation so it says**

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 x x2 Our answer should say ... p = 2(m – n)

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**Example more difficult**

Rearrange the equation a = x to make x the subject. a = x + 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 x = divide by (d + c)

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**Example more difficult**

Rearrange the equation a = + to make p the subject. a = + 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 p = divide by (aq – 1)

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**Example more 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 p(a – b) = b + c – a factorise p = divide by (a – b)

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**Example more 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

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**Test Yourself 1. Rearrange the equation a = x + to make x the subject.**

Check your answers on previous slides Test Yourself 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. 4. Rearrange the equation s = b + to make t the subject.

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