Questions: Introduction to rearranging equations
Before attempting these questions, it is highly recommended that you read Guide: Introduction to rearranging equations.
Q1
For each of the following equations, rearrange the equation for the variable given.
1.1. Rearrange \(x = a + 2b\) for \(a\).
1.2. Rearrange \(x = a + 2b\) for \(b\).
1.3. Rearrange \(x - 2y + 4z = 4\) for \(z\).
1.4. Rearrange \(5x - 3y + 8z = -2\) for \(x\).
1.5. Rearrange \(5x - 3y + 8z = -2\) for \(y\).
1.6. Rearrange \(5x - 3y + 8z = -2\) for \(z\).
1.7. Rearrange \(x^2 + y^2 = 4\) for \(x\).
1.8. Rearrange \(\dfrac{x^2}{4} + \dfrac{y^2}{16} = a\) for \(x\).
1.9. Rearrange \(\dfrac{x^2}{4} + \dfrac{y^2}{16} = a\) for \(y\).
1.10. Rearrange \(\sqrt{x^2 - a^2} = y + 1\) for \(x\).
1.11. Rearrange \(\sqrt[3]{x^3 - a^3} = y + 1\) for \(a\).
1.12. Rearrange \(\sqrt[3]{x^3 - a^3} = y + 1\) for \(x\).
1.13. Rearrange \(x^4y^2 = a^3 + 2bcd\) for \(d\).
1.14. Rearrange \(x^4y^2 = a^3 + 2bcd\) for \(a\).
1.15. Rearrange \(x^4y^2 = a^3 + 2bcd\) for \(x\).
1.16. Rearrange \(\dfrac{1}{x} + 45 = ly^2\) for \(x\).
Q2
In Guide: Introduction to rearranging equations, you saw the expression \[5x^3y^3 + \frac{6z}{w^4} = 4abc^2\] where you rearranged this equation for \(x\).
Rearrange this expression for every other variable \(a,b,c,y,z,w\).
After attempting the questions above, please click this link to find the answers.
Version history and licensing
v1.0: initial version created 08/23 by Shanelle Advani and tdhc as part of a University of St Andrews STEP project.
- v1.1: edited 05/24 by tdhc.