Question

Solve T=C(8+AB) for A

Answer 1

`\begin{gathered} \text{Given} \\ T=C(8+AB) \end{gathered}`
`\begin{gathered} \text{Divide both sides by }C \\ T=C(8+AB) \\ (T)/(C)=(C(8+AB))/(C) \\ (T)/(C)=\frac{\cancel{C}(8+AB)}{\cancel{C}} \\ (T)/(C)=8+AB \\ \\ \text{Subtract both sides by }8 \\ (T)/(C)-8=8-8+AB \\ (T)/(C)-8=\cancel{8-8}+AB \\ (T)/(C)-8=AB \\ \\ \text{Divide both sides by }B \\ ((T)/(C)-8)/(B)=(AB)/(B) \\ ((T)/(C))/(B)-(8)/(B)=\frac{A\cancel{B}}{\cancel{B}} \\ (T)/(CB)-(8)/(B)=A \\ \\ \text{By symmetric property of equality, we can swap left and right side of equations} \\ (T)/(CB)-(8)/(B)=A \\ A=(T)/(CB)-(8)/(B) \end{gathered}`