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Inequalities

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Inequalities

The inequalities section of QuickMath allows you to solve virtually any inequality or system of inequalities in a single variable. In most cases, you can find exact solutions. Even when this is not possible, QuickMath may be able to give you approximate solutions to almost any level of accuracy you require. In addition, you can plot the regions satisfied by one or more inequalities in two variables, seeing clearly where the intersections of those regions occur.

What are inequalities?

Inequalities consist of two or more algebraic expressions joined by inequality symbols. The inequality symbols are :

< less than
> greater than
<= less than or equal to
>= greater than or equal to
!= or <> not equal to

Here are a few examples of inequalities :

2 x - 9 > 0

x2 - 3 x + 5 <= 0

| 5x - 1 | <> 5

x3 + 1 <= 0

Solve

The Solve command can be used to solve either a single inequality for a single unknown from the basic solve page or to simultaneously solve a system of many inequalities in a single unknown from the advanced solve page. The advanced command allows you to specify whether you want approximate numerical answers as well as exact ones, and how many digits of accuracy (up to 16) you require.

Multiple inequalities in the advanced section are taken to be joined by AND. For example, the inequalities

2 x - 1 > 0
x^2 - 5 < 0

on two separate lines in the advanced section are read by QuickMath as

2 x - 1 > 0 AND x^2 - 5 < 0

In other words, QuickMath will try to find solutions satisfying both inequalities at once.

Go to the Solve page

Plot

The Plot command, from the Graphs section, will plot any inequality involving two variables. In order to plot the region satisfied by a single inequality involving x and y, go to the basic inequality plotting page, where you can enter the inequality and specify the upper and lower limits on x and y that you want the graph to be plotted for. The advanced inequality plotting page allows you to plot the union or intersection of up to 8 regions on the one graph. You have control over such things as whether or not to show the axes, where the axes should be located and what the aspect ratio of the plot should be. In addition, you have the option of showing each individual region on its own.

Go to the Inequalities Plotting page

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