Changing the subject where the variable appears in multiple terms

12 questions

1. In which of these is x the subject?
2. Make x the subject of 3x+4=5x-b.
3. Factorise x^2 - 6x + 8.
4. Shown is the formula for the perimeter of a rectangle. Make b the subject.
5. Make z the subject of \frac{4}{x} +\frac{2}{y} = \frac{3}{z}.
6. Simplify \frac{3x-12}{2x-6} + \frac{x}{3x-9}
7. What is the most efficient first step to make x the subject of ax + b = 2x + c?
8. What is the most efficient next step to make x the subject of ax-2x = c-b ?
9. Make a the subject of a(b+c)=3+4(a+2b).
10. Make r the subject of p = \frac{r+5}{r+q}.
11. What would be the most efficient first step to make a the subject of \frac{8a+4b}{6a+3b}+\frac{a+1}{3a+3b}=b ?
12. Make a the subject of \frac{4(2a+b)}{3(2a+b)}+\frac{a+1}{3(a+b)}=b.

License: OGL