# Questions tagged [inequalities]

Questions about handling with inequalities with, e.g., Reduce, Solve, FindInstance etc., their application in defining Regions, and ways to incorporate them into other computations, e.g. integration.

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### Is it possible to have Mathematica move all terms to one side of an inequality?

I have an inequality expression that I would like to express in terms of the relation of the parameters to zero. More simply, I want to have mathematica move all the terms to one side of the ...
259 views

### Checking inequalities: How can $x>0,y>0$ yet $x+y$ indeterminate?

I have the following: ...
3k views

### Trying to prove that $x\sin(\frac{\pi}{x})\ge\pi \cos(\frac{\pi}{x})$ for $x\ge 1$

As an intermediate step, consider the function: f[x_] := x Sin[Pi/x] I want to prove that this function is increasing for $x\ge 1$. This can be done with the ...
1k views

### Converting inequalities to intervals

I have an inequality, ie: 1.57116 < g < 14.1405 There will be a large set of similar inequalities, and I want to find the intersection of them all. I figured it would be easier to convert the ...
2k views

### Shading a region where an inequality is satisfied

Bug introduced in 9.0 or earlier and persisting through 11.0.1 or later I'm creating solution sets for a calculus course and need to shade the region in $\mathbb R^2$ such that $x^2 < y < x^4$. ...
144 views

### Reduce time taken to get feasible solution [closed]

I have such a set of nonlinear inequalities with m variables, Please suggest some good method to get some feasible solutions, where a[i]'s belong to [-5,5].So please suggest an approach, to get ...
89 views

### Make Reduce produce nicer output

I am trying to reduce a bunch of inequalities using the Reduce command in Mathematica. But the output is very convoluted and I am wondering if there's a way to systematically organize it so that I can ...
184 views

### Solve for parameters so that a relation is always satisfied

Let's say I have a function parameterized by a number of variables. As a simple example $$F(x,y) = ax^2 +by^2-cxy+1$$ I want to find some set of values (doesn't really matter what they are) for the ...
2k views

### Find the volume of the region defined by $|x|+|y|+|z|<4$

I want to find the volume of the region defined by the following inequality: $\quad \quad |x|+|y|+|z|<4$ In addition to calculating the volume of this region, I would also like to be able to ...
111 views

### Inequality involving Quantity stays unevaluated

Bug introduced in 10.1 and solved in 11.1 An expression like this one a < x < b is represented as Less[a, x, b] ...
136 views

### How to represent in a 3D graph the set of solutions to this system of inequalities?

I am studying this piecewise function: ...
202 views

### Evaluating an Inequality

I am evaluating a parametric inequality conditional on some assumptions on the parameters. In the simplest form, here, I am assuming the numerator and the denominator are positive: ...
91 views

### How to get solutions for this system of inequalities?

I am new to Mathematica and I am struggling finding the solution for the following problem. I am studying this piecewise function: ...