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An equation is any valid mathematical statement that includes an equals sign (=). For example:

One of the key tasks in algebra is to solve equations. Usually, that means discovering the value of the variable in that equation.

In some cases, an equation is true for all (or just about all) values of the variable. An equation like this is called an identity. For example:

The first two identities are true for all values of x. The third is true for all values of x except 0, because a value of 0 in the denominator is not allowed. Identities can be helpful because they allow you to rewrite, and even rethink, an equation in a different and potentially more helpful form.

Finally, an inequality is a valid mathematical statement that includes one of four inequality operators: less than (<), greater than (>), less than or equal to (), and greater than or equal to (). For example:

You can’t usually solve an inequality for a specific value, as you can with an equation. Rather, an inequality is usually solved for a solution set — that is, a set of values that satisfy the inequality. For example, the solution set for the first inequality is (,5), which is the set of numbers less than (that is, up to but not including) 5.