You solve an inequality in exactly the same was as you solve an equation, by doing the same thing to both sides. The only difference is if you multiply/divide by a negative number, when you have to turn the inequality around.
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It is important to know several techniques for solving equations and inequalities because one may work better than another in a particular situation.
it often simplifies arithmetic
Study everything - that's your best bet. Important subjects probably include: Polynomials, Exponents, Radicals, Solving Equations, Solving Inequalities, Absolute Value Equations and Inequalities, Lines, Word Problems, Systems of Equations (2x2's), Factoring, Division of Polynomials, Quadratics, Parabolas, Complex Numbers, Algebraic Fractions, Functions
Just keep doing the same thing to both sides of the equation at every step.
equations have an = sign, inequalities do not