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Inequalities : Solve

Basic | Intermediate | Advanced | Help

Description

The solve command will solve single inequalities or systems of inequalities. It can handle almost any inequality found in high school math courses. The solve command will always try to give an exact solution, although this may not always be possible. Some inequalities, such as those containing polynomials of degree higher than 5, cannot be solved exactly. In cases like this, QuickMath will attempt to give numerical approximations (of up to 16 digits accuracy) whenever possible. Some inequalities, such as those involving trigonometric or logarithmic functions, may have an infinite number of solutions. Whenever QuickMath cannot find all the solutions of an inequality or system of inequalities like this, it will warn you that not all solutions are being found.

To use the solve command on a single inequality, simply go to the basic solve page, type in your inequality along with the variable you would like to solve it for and hit the "Solve" button. Your question will be automatically answered by computer and the reply will be shown in your browser within a few seconds. If you would like to solve a system of inequalities simultaneously, try the advanced solve page. Enter one inequality per line (separated by carriage returns) in the Inequalities text area, enter the variable you wish to solve for in the Variable text area and decide whether you want exact solutions only or approximations as well. Then simply hit the "Solve" button and your question will be answered right away.

Examples

Here are some examples illustrating the types of expressions you can use the inequalities solve command on and the results which QuickMath will return.

Basic
Inequality Variable Result
5x-3>7 x x > 2
2x-4<3x+1 x x > -5
x^2<=4 x -2 <= x <= 2
x <> 1 x x < 1 OR x > 1
Advanced
Inequalities Variable Result
4x+2>13
2x-1<23
x 3 < x < 12
e^x<10
x<>1
x x < 1 OR 1 < x < log(10)
x^4-5x^2-1>0 x

          5 + sqrt(29)
x < -sqrt(------------)
               2

OR

         5 + sqrt(29)
x > sqrt(------------)
               2

Options (advanced page only)

Approximate

Values : checked or unchecked + empty string or non-negative integer
Default : checked + 6

When Approximate is checked, the solutions will be presented to the specified number of digits, as well as in exact form if possible.