# How to solve inequalities of this kind?

**URL:** <https://discourse.julialang.org/t/how-to-solve-inequalities-of-this-kind/96404>\
**Category:** General Usage\
**Tags:** symbolics\
**Created:** [March 21, 2023, 5:21pm UTC](https://discourse.julialang.org/t/how-to-solve-inequalities-of-this-kind/96404 "2023-03-21T17:21:12Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![jcbritobr](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jcbritobr/32/219275_2.png) [@jcbritobr](https://discourse.julialang.org/u/jcbritobr)\
**Post date:** [March 21, 2023, 5:21pm UTC](https://discourse.julialang.org/t/how-to-solve-inequalities-of-this-kind/96404/1 "2023-03-21T17:21:12Z")

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Hello, good afternoon

How to solve inequalities of this kind?

```julia
4 <= 3x - 2 < 13

```

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<div class="post-metadata">

**Author:** ![empet](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/empet/32/221303_2.png) [@empet](https://discourse.julialang.org/u/empet)\
**Post date:** [March 21, 2023, 7:11pm UTC](https://discourse.julialang.org/t/how-to-solve-inequalities-of-this-kind/96404/2 "2023-03-21T19:11:02Z")

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See this thread [https://discourse.julialang.org/t/solving-inequations/58410](https://discourse.julialang.org/t/solving-inequations/58410).

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<div class="post-metadata">

**Author:** ![jcbritobr](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jcbritobr/32/219275_2.png) [@jcbritobr](https://discourse.julialang.org/u/jcbritobr)\
**Post date:** [March 21, 2023, 7:49pm UTC](https://discourse.julialang.org/t/how-to-solve-inequalities-of-this-kind/96404/3 "2023-03-21T19:49:52Z")

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I saw it when searching for a solution, but it has not has two inequalities. Then I found something in Python group.

```julia
x = sp.symbols('x')

s1 = sp.solve_univariate_inequality(4 <= 3*x - 2, x)
s2 = sp.solve_univariate_inequality(3*x - 2 < 13, x)
s1 & s2

```

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<div class="post-metadata">

**Author:** ![j\_verzani](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/j_verzani/32/8551_2.png) [@j\_verzani](https://discourse.julialang.org/u/j_verzani)\
**Post date:** [March 21, 2023, 9:04pm UTC](https://discourse.julialang.org/t/how-to-solve-inequalities-of-this-kind/96404/4 "2023-03-21T21:04:59Z")

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For completeness, within `Julia`, the same can be done with `SymPy` as:

```julia
@syms x::real
u = solve(Lt(4, 3x-2), x) & solve(3x-2 ≦ 12,x) # \leqq[tab] is infix unicode for Lt
u.as_set()

```

The latter conversion allows you to query, as in ` 3 ∈ u.as_set()`