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(sqrt14-4)*x<0 inequation

A inequation with variable

The solution

You have entered [src]
/  ____    \      
\\/ 14  - 4/*x < 0
x(4+14)<0x \left(-4 + \sqrt{14}\right) < 0
x*(-4 + sqrt(14)) < 0
Detail solution
Given the inequality:
x(4+14)<0x \left(-4 + \sqrt{14}\right) < 0
To solve this inequality, we must first solve the corresponding equation:
x(4+14)=0x \left(-4 + \sqrt{14}\right) = 0
Solve:
Given the linear equation:
(sqrt(14)-4)*x = 0

Expand brackets in the left part
sqrt+14-4)*x = 0

Move free summands (without x)
from left part to right part, we given:
x(4+14)+4=4x \left(-4 + \sqrt{14}\right) + 4 = 4
Divide both parts of the equation by (4 + x*(-4 + sqrt(14)))/x
x = 4 / ((4 + x*(-4 + sqrt(14)))/x)

x1=0x_{1} = 0
x1=0x_{1} = 0
This roots
x1=0x_{1} = 0
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
x0<x1x_{0} < x_{1}
For example, let's take the point
x0=x1110x_{0} = x_{1} - \frac{1}{10}
=
110- \frac{1}{10}
=
110- \frac{1}{10}
substitute to the expression
x(4+14)<0x \left(-4 + \sqrt{14}\right) < 0
(1)(4+14)10<0\frac{\left(-1\right) \left(-4 + \sqrt{14}\right)}{10} < 0
      ____    
2   \/ 14     
- - ------ < 0
5     10      
    

but
      ____    
2   \/ 14     
- - ------ > 0
5     10      
    

Then
x<0x < 0
no execute
the solution of our inequality is:
x>0x > 0
         _____  
        /
-------ο-------
       x1
Solving inequality on a graph
-5.0-4.0-3.0-2.0-1.05.00.01.02.03.04.00.2-0.1
Rapid solution [src]
And(0 < x, x < oo)
0<xx<0 < x \wedge x < \infty
(0 < x)∧(x < oo)
Rapid solution 2 [src]
(0, oo)
x in (0,)x\ in\ \left(0, \infty\right)
x in Interval.open(0, oo)