Third Space Learning Rearranging Equations GCSE Worksheet | PDF ... - Free Printable

Final Answer:
1) $ a = c - b $
2) $ a = c - b $
3) $ a = -2b - c $
4) $ a = \frac{c + b}{2} $
5) $ a = \frac{b - c}{2} $
6) $ a = \frac{-b - 2c}{2} $
7) $ a = bc $
8) $ a = 2bc $
9) $ a = 2b(c +) $

Group B:
1) $ m = \sqrt{n} $ (or $ m = -\sqrt{n} $, but usually positive root unless stated)
2) $ m = \sqrt{n - 5} $
3) $ m = \sqrt{6n} + 10 $
4) $ m = np - 3 $
5) $ m = np - 3 $
6) $ m = \frac{p}{n} - 3 $
7) $ m = n $
8) $ m = 2 $
9) $ m = \frac{10}{4} = \frac{5}{2} $

Group C:
1) $ x = \frac{1}{y - 1} $
2) $ x = \frac{x + 1}{y} $ → better: multiply both sides by $x$: $ xy = x + 1 $, then $ xy - x = 1 $, so $ x(y - 1) = 1 $, thus $ x = \frac{1}{y - 1} $
Wait — actually, for Group C, all ask to make x the subject. Let’s correct each carefully:

1) $ xy = x + 1 $
→ $ xy - x = 1 $
→ $ x(y - 1) = 1 $
→ $ x = \frac{1}{y - 1} $

2) $ y = \frac{x + 1}{x} $
→ $ y = 1 + \frac{1}{x} $
→ $ y - 1 = \frac{1}{x} $
→ $ x = \frac{1}{y - 1} $

3) $ y = \frac{x + 2}{x + 1} $
→ $ y(x + 1) = x + 2 $
→ $ yx + y = x + 2 $
→ $ yx - x = 2 - y $
→ $ x(y - 1) = 2 - y $
→ $ x = \frac{2 - y}{y - 1} $ or $ x = \frac{y - 2}{1 - y} $

4) $ 2y + 1 = \frac{x + 1}{x} $
→ RHS = $1 + \frac{1}{x}$ so:
$ 2y + 1 = 1 + \frac{1}{x} $
→ $ 2y = \frac{1}{x} $
→ $ x = \frac{1}{2y} $

5) $ 2y = \frac{2x + 3}{x} - 1 = \frac{2x + 3 - x}{x} = \frac{x + 3}{x} = 1 + \frac{3}{x} $
→ $ 2y - 1 = \frac{3}{x} $
→ $ x = \frac{3}{2y - 1} $

6) $ y^2 = \frac{x + 4}{x} = 1 + \frac{4}{x} $
→ $ y^2 - 1 = \frac{4}{x} $
→ $ x = \frac{4}{y^2 - 1} $

7) $ y = \frac{ax}{a - x} $
→ $ y(a - x) = ax $
→ $ ay - yx = ax $
→ $ ay = ax + yx = x(a + y) $
→ $ x = \frac{ay}{a + y} $

8) $ \frac{3x + 2}{y} = \frac{x + 1}{z} $
→ cross-multiply: $ z(3x + 2) = y(x + 1) $
→ $ 3zx + 2z = yx + y $
→ $ 3zx - yx = y - 2z $
→ $ x(3z - y) = y - 2z $
→ $ x = \frac{y - 2z}{3z - y} $

9) $ y = \frac{z^2 + x}{z + x} $
→ $ y(z + x) = z^2 + x $
→ $ yz + yx = z^2 + x $
→ $ yx - x = z^2 - yz $
→ $ x(y - 1) = z(z - y) $
→ $ x = \frac{z(z - y)}{y - 1} $

But since the instruction says: *ExplainAnswer: false*, *TeachTopic: false*, *GeneratePractice: false*, we only give the final answer — and only the correct simplified forms, as expected in GCSE level.

However, the user expects only the final correct answer, no explanation. So list only the answers per question in order, clearly labeled.

Let me compile the final answers concisely as a single block (as per format):

Final Answer:
Group A:
1) $ a = c - b $
2) $ a = c - b $
3) $ a = -2b - c $
4) $ a = \dfrac{c + b}{2} $
5) $ a = \dfrac{b - c}{2} $
6) $ a = \dfrac{-b - 2c}{2} $
7) $ a = bc $
8) $ a = 2bc $
9) $ a = 2b(c + 2) $

Group B:
1) $ m = \sqrt{n} $
2) $ m = \sqrt{n - 5} $
3) $ m = \sqrt{6n} + 10 $
4) $ m = np - 3 $
5) $ m = np - 3 $
6) $ m = \dfrac{p}{n} - 3 $
7) $ m = n $
8) $ m = 2 $
9) $ m = \dfrac{5}{2} $

Group C:
1) $ x = \dfrac{1}{y - 1} $
2) $ x = \dfrac{1}{y - 1} $
3) $ x = \dfrac{2 - y}{y - 1} $
4) $ x = \dfrac{1}{2y} $
5) $ x = \dfrac{3}{2y - 1} $
6) $ x = \dfrac{4}{y^2 - 1} $
7) $ x = \dfrac{ay}{a + y} $
8) $ x = \dfrac{y - 2z}{3z - y} $
9) $ x = \dfrac{z(z - y)}{y - 1} $