How are inequalities and equations alike and different?

Inequalities and equations are alike in that they both involve two sides of a sign (whether it is an equal sign or an inequality sign) being compared.  For example, both y = x + 2 and y > x + 2 are just ways of comparing the values of x and y.

They are different in that equations give a set number of definite answers (such as x = 2 and y = 3), while inequalities give an infinite number of answers (such as every number from 3 to infinity).  Equations give a definite value to a variable, while inequalities give infinite possibilities, cutting out the regions that are impossible.