# 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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### How to find a set of solution of the inequality?

There exists a,b,c,d,e such that ...
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I used ...
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### Solving a set of trig inequalities

I have a set of inequalities Cos[a]Cos[b]>=Cos[t-a]Cos[b]&&Cos[a]Cos[b]>=Cos[t/2]&&Cos[a]Cos[b]>=Sin[t/2]&&a<=t<=Pi How to ...
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### How to prove or disprove an inequality with Mathematica?

I mean there exist $\lambda>0, x\in \mathbb R$ s.t. the inequality $$\frac{3^{\lambda } e^x+e^{3 x}+1}{2^{\lambda } e^{2 x}}<\frac{1}{10^{100}}$$ is valid. Here are my unsuccessful attempts. <...
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### Why does MMA fail to find a solution but WA does?

I am looking for $n$, where $$\dfrac{2^{-3 n-2} \pi ^{n+1}}{(n+1)!}<\dfrac{1}{10000000000000000}$$ We can just test values of $n$ and find the smallest $n = 13$, or any $n \gt 13$ or can use ...
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### While Loop inside a Do loop and the usage of a break

I am struggling with using a While loop inside a Do loop and using the break to break the loop. In this code, I would like to use the While loop for the value of i and the Do loop for the value of h, ...
1 vote
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### Reduce works for simple inequalities in Reals but not in Integers

In the domain of Reals Reduce correctly reduces the system to True: ...
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### Reduce an inequality

I have this inequality I don't know why it is not working?! ...
1 vote
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1 vote
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### How to prove the inequality of undefined function?

For example, how to prove the following inequality? ...
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### Regarding validity of expressions involving inequalities

This expression is valid: $$\left|\log(1+x) - \log(1 - x)\right| \leq \frac{\left|x-y\right|}{1+|x-y|},\ \ 0<x<1, \ 0<y<1$$ How we can prove using Mathematica (either graphically or ...
291 views

### How to simplify one side of an inequality with a lot of square roots that are the same

Mathematica seems to refuse to simplify the following inequality, even though it is obvious there are things that can be done ...
I want to find $a,b \in \mathbb{C}$ such that $$|1-2a-2b| < 1 \quad \text{&} \quad |1-2a+2b| < 1$$ using mathematica. I tried to use ...