How do you do inequations?

Answer 1

By "inequations" I assume you mean "inequalities" because I can't think of anything else other than equations where the equation sign is crossed, and I don't think you mean that.

Most algebraic operations work the same in equations and inequalities; one thing to be wary with is multiplying or dividing both sides of an inequality by a negative number. Take the inequality 3 < 4. If you multiply both sides by -1, you get -3 < -4, which is incorrect; so, when you multiply or divide both sides of an inequality, be sure to invert the inequality sign.

Also, when the sign of an algebraic expression is ambiguous, I sometimes use the square of the expression, as the square of an algebraic expression not involving complex numbers will be positive; I do this to be a bit "surer" of the sign. However, this may introduce more problems, of which extraneous solutions are only the tip of the iceberg.

Sorry for the rather unnecessarily verbose answer.