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The package provides a function for solving systems of inequalities. InequalitySolve[expr, x] finds conditions that must be satisfied by real values of x in order for the expression expr to be true. The expression should contain logical connectives and polynomial equations and inequalities in the specified variable.

Finding solutions to inequalities.

This loads the package.

In[1]:= <<Algebra`InequalitySolve`

Here is a set of solutions to a polynomial inequality.

In[2]:= InequalitySolve[x (x^2 - 2) (x^2 - 3) > 0, x]


The inequalities may contain absolute values and rational functions.

In[3]:= InequalitySolve[x/Abs[x - 1] >= 0 && 1/x < x + 1, x]


Multivariate inqualities may also be solved.

In[4]:= InequalitySolve[x^2 + y^2 < 1 && x < y, {x, y}]


Here the inequalities contain the exponential function. In general, if inequalities contain nonpolynomial functions of the specified variable, you may get an incorrect result.

In[5]:= InequalitySolve[Abs[x - 1] <= 5 && E^x <= 3, x]