Add the additive inverse of any terms in the LHS that do NOT contain the desired variable to both sides. Add the additive inverse of any terms in the RHS that DO contain the desired variable to both sides. Combine like terms. Factor the desired variable from any multi-term expression that remains in the LHS. Multiply by the reciprocal of the resulting coefficient on the desired variable.
If you have a quadratic, put it into standard form then either factor it or use the quadratic formula. If you have a cubic or quartic, look for rational roots or use the general cubic or quartic solution. If you have a higher degree polynomial equation, use the rational roots theorem and synthetic division to find enough rational factors to reduce the degree to no more than 4. Barring that, use numerical approximation methods such as Newton-Raphson.
If the desired variable is included in an exponent, take the log of both sides. If the desired variable is in a log argument, use the laws of logs to combine into a single log expression and then use the definition of logs.
That should cover most situations that you will encounter in Algebra I and II, and about the best I can do to teach two years of mathematics in this little text box.
John
My calculator said it, I believe it, that settles it
