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. Whatever you do to one side of the equals sign you must do to the other.

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

This means we want to rearrange the equation so it says 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

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

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

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

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

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)

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)

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)

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

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.