Question

How are inequalities and equations alike and different?

Answer 1

You can solve inequalities in the same way you can solve equations. You may add any positive or negative number to both sides of an inequality. You may also  multiply or divide both sides of an inequality by any positive number.
Inequalities have <, >, >, < and equation have an equal sign.

Answer 2

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.