Many inequalities can be solved by simply adding, subtracting, multiplying and dividing both sides until the variable is by itself. It is important to remember that multiplying or dividing both sides by a negative number will reverse the inequality.
- Set up the problem
When dealing with inequalities, the point of the problem is to get the variable by itself on one side of the equation. A standard example of an inequality is 4 - 2X > 14. This equation is relatively straightforward but provides good examples of the types of issues dealt with when solving inequalities.
- Remove the constant value
Adding and subtracting to remove the constant value is an easy and safe way to make the problem more manageable and to allow further advancement. In the example equation, start by eliminating the 4 from the variable side of the equation by subtracting 4 from both sides; this results in the equation -2X > 10.
- Multiply and divide to isolate the variable
The final step is multiplying or dividing to get the variable by itself. In the example equation, simply divide by the negative 2 on both sides to solve for X, which is equal to anything less than -5. Remember that when dividing or multiplying by a negative, you must reverse the direction of the inequality sign.