Inequalities are a little different from regular equations because your answer may not be just one single number.
Instead, the answers to problems of algebra inequalities are ranges of numbers. The inequality is simply a way of showing that the range of values will all satisfy the equation. The word "inequality" in a this mathematical sense is basically telling you that the equation will have < and >'s (less than, greater than) signs instead of simply an equals (=) sign.
Let's take a look:
X + 3 > 5
This is saying that the answer is all numbers (X) that when added to 3, is greater than 5. You need to find which numbers make that statement true. While you could guess on the easy ones, it's always best to have a foolproof way to find them ALL. (Hint: The answer is not X=2.)
Step 1: Isolate X as you would do in any standard algebra equation.
Step 2: For addition and subtraction, that's all you need to do. For division, you also need to use the inverse equality - that is, > turns into <, and < turns to >!
All the normal rules for solving equations still apply. You can subtract to cancel out additions (and vice versa), and you can multiply to cancel divisions (and vice versa.) Always remember, whatever you do to one side of the inequality, you MUST do to the other side to keep the statement true!
Ready to try some? You'll find that they're pretty easy! (Answers below)
1. X + 2 < 12
2. X * 4 > 16
3. X / 2 < 12
4. X - 2 > 18
Here are the answers worked out:
As you have probably noticed, solving inequalities is much like solving standard equality equations! There really is not much to it!
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