Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- y^2-4*x+8>0
-
(|x+3|)+4*x>=6
- (sqrt(3)-(sqrt(13)))x>5/(sqrt(3)+sqrt(13))
- logx+1,(x-2)<=1
-
Identical expressions
- (sqrt(three)-(sqrt(thirteen)))x> five /(sqrt(three)+sqrt(thirteen))
- ( square root of (3) minus ( square root of (13)))x greater than 5 divide by ( square root of (3) plus square root of (13))
- ( square root of (three) minus ( square root of (thirteen)))x greater than five divide by ( square root of (three) plus square root of (thirteen))
- (√(3)-(√(13)))x>5/(√(3)+√(13))
- sqrt3-sqrt13x>5/sqrt3+sqrt13
- (sqrt(3)-(sqrt(13)))x>5 divide by (sqrt(3)+sqrt(13))
-
Similar expressions
- (sqrt(3)+(sqrt(13)))x>5/(sqrt(3)+sqrt(13))
- (sqrt(3)-(sqrt(13)))x>5/(sqrt(3)-sqrt(13))
(sqrt(3)-(sqrt(13)))x>5/(sqrt(3)+sqrt(13)) inequation
The solution
You have entered
[src]
/ ___ ____\ 5
\\/ 3 - \/ 13 /*x > --------------
___ ____
\/ 3 + \/ 13
$$x \left(- \sqrt{13} + \sqrt{3}\right) > \frac{5}{\sqrt{3} + \sqrt{13}}$$
x*(-sqrt(13) + sqrt(3)) > 5/(sqrt(3) + sqrt(13))
Detail solution
Given the inequality:
$$x \left(- \sqrt{13} + \sqrt{3}\right) > \frac{5}{\sqrt{3} + \sqrt{13}}$$
To solve this inequality, we must first solve the corresponding equation:
$$x \left(- \sqrt{13} + \sqrt{3}\right) = \frac{5}{\sqrt{3} + \sqrt{13}}$$
Solve:
Given the linear equation:
Expand brackets in the left part
Expand brackets in the right part
Divide both parts of the equation by sqrt(3) - sqrt(13)
$$x_{1} = - \frac{1}{2}$$
$$x_{1} = - \frac{1}{2}$$
This roots
$$x_{1} = - \frac{1}{2}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{2} + - \frac{1}{10}$$
=
$$- \frac{3}{5}$$
substitute to the expression
$$x \left(- \sqrt{13} + \sqrt{3}\right) > \frac{5}{\sqrt{3} + \sqrt{13}}$$
$$\frac{\left(-3\right) \left(- \sqrt{13} + \sqrt{3}\right)}{5} > \frac{5}{\sqrt{3} + \sqrt{13}}$$
the solution of our inequality is:
$$x < - \frac{1}{2}$$
$$x \left(- \sqrt{13} + \sqrt{3}\right) > \frac{5}{\sqrt{3} + \sqrt{13}}$$
To solve this inequality, we must first solve the corresponding equation:
$$x \left(- \sqrt{13} + \sqrt{3}\right) = \frac{5}{\sqrt{3} + \sqrt{13}}$$
Solve:
Given the linear equation:
(sqrt(3)-(sqrt(13)))*x = 5/(sqrt(3)+sqrt(13))
Expand brackets in the left part
sqrt+3-sqrt-13))*x = 5/(sqrt(3)+sqrt(13))
Expand brackets in the right part
sqrt+3-sqrt-13))*x = 5/sqrt+5/3+sqrt13)
Divide both parts of the equation by sqrt(3) - sqrt(13)
x = 5/(sqrt(3) + sqrt(13)) / (sqrt(3) - sqrt(13))
$$x_{1} = - \frac{1}{2}$$
$$x_{1} = - \frac{1}{2}$$
This roots
$$x_{1} = - \frac{1}{2}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{2} + - \frac{1}{10}$$
=
$$- \frac{3}{5}$$
substitute to the expression
$$x \left(- \sqrt{13} + \sqrt{3}\right) > \frac{5}{\sqrt{3} + \sqrt{13}}$$
$$\frac{\left(-3\right) \left(- \sqrt{13} + \sqrt{3}\right)}{5} > \frac{5}{\sqrt{3} + \sqrt{13}}$$
___ ____ 5
3*\/ 3 3*\/ 13 --------------
- ------- + -------- > ___ ____
5 5 \/ 3 + \/ 13
the solution of our inequality is:
$$x < - \frac{1}{2}$$
_____
\
-------ο-------
x1
Solving inequality on a graph
Rapid solution 2
[src]
(-oo, -1/2)
$$x\ in\ \left(-\infty, - \frac{1}{2}\right)$$
x in Interval.open(-oo, -1/2)
Rapid solution
[src]
And(-oo < x, x < -1/2)
$$-\infty < x \wedge x < - \frac{1}{2}$$
(-oo < x)∧(x < -1/2)