Lesson: Basic Algebra - 08

Introducing Inequalities

Variables can also occur in inequalities. An inequality is a statement of the relative size of quantities, and when only straight numbers are involved, inequalities are self-evident, e.g. 10 > 5, or 88 < 102. But when inequalities involve variables they can become confusing. div>

Think of a variable in an inequality as representing a range of numbers.
You may use the same solution methods for inequalities as you use for equations (with one big exception, which we'll discuss in a minute). In general, what you do with an inequality is to isolate the variable to one side, as in:

See what we mean by "a variable in an inequality is a range"? In this example, x can be equal to any number less than –3. In other words, any number less than –3 will make the inequality true. For example, if x were equal to – 4, then:

Since the inequality is valid, we have proven that x could be equal to – 4, and of course it could be equal to a lot of other numbers, too. But x cannot be equal to –3, for if it were, the two sides would be equal. And x cannot be greater than –3, because then the left side would be greater than the right.

All the rules for solving equations apply to solving inequalities as well: do the same thing to both sides, don’t multiply by zero, and don’t multiply by a variable.

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