Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- 4(x-5)>=3/(x+2)
- 1/3-x/2^2>sqrt(3)
- (x^2+3^x-3)^5>(x^2+9^x-3^x)*5
- 4x−3x**2−9≤0
- Derivative of:
-
sqrt(3)
- Integral of d{x}:
-
sqrt(3)
- Limit of the function:
-
sqrt(3)
-
Identical expressions
- one / three -x/ two ^ two >sqrt(three)
- 1 divide by 3 minus x divide by 2 squared greater than square root of (3)
- one divide by three minus x divide by two to the power of two greater than square root of (three)
- 1/3-x/2^2>√(3)
- 1/3-x/22>sqrt(3)
- 1/3-x/22>sqrt3
- 1/3-x/2²>sqrt(3)
- 1/3-x/2 to the power of 2>sqrt(3)
- 1/3-x/2^2>sqrt3
- 1 divide by 3-x divide by 2^2>sqrt(3)
-
Similar expressions
- 1/3+x/2^2>sqrt(3)
- cos(2x)<(sqrt3)/2
- cos>=-sqrt3/2
1/3-x/2^2>sqrt(3) inequation
The solution
You have entered
[src]
1 x ___ - - - > \/ 3 3 4
$$- \frac{x}{4} + \frac{1}{3} > \sqrt{3}$$
-x/4 + 1/3 > sqrt(3)
Detail solution
Given the inequality:
$$- \frac{x}{4} + \frac{1}{3} > \sqrt{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$- \frac{x}{4} + \frac{1}{3} = \sqrt{3}$$
Solve:
Given the linear equation:
Expand brackets in the right part
Move free summands (without x)
from left part to right part, we given:
$$- \frac{x}{4} = - \frac{1}{3} + \sqrt{3}$$
Divide both parts of the equation by -1/4
$$x_{1} = \frac{4}{3} - 4 \sqrt{3}$$
$$x_{1} = \frac{4}{3} - 4 \sqrt{3}$$
This roots
$$x_{1} = \frac{4}{3} - 4 \sqrt{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\frac{4}{3} - 4 \sqrt{3}\right) + - \frac{1}{10}$$
=
$$\frac{37}{30} - 4 \sqrt{3}$$
substitute to the expression
$$- \frac{x}{4} + \frac{1}{3} > \sqrt{3}$$
$$\frac{1}{3} - \frac{\frac{37}{30} - 4 \sqrt{3}}{4} > \sqrt{3}$$
the solution of our inequality is:
$$x < \frac{4}{3} - 4 \sqrt{3}$$
$$- \frac{x}{4} + \frac{1}{3} > \sqrt{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$- \frac{x}{4} + \frac{1}{3} = \sqrt{3}$$
Solve:
Given the linear equation:
1/3-x/2^2 = sqrt(3)
Expand brackets in the right part
1/3-x/2^2 = sqrt3
Move free summands (without x)
from left part to right part, we given:
$$- \frac{x}{4} = - \frac{1}{3} + \sqrt{3}$$
Divide both parts of the equation by -1/4
x = -1/3 + sqrt(3) / (-1/4)
$$x_{1} = \frac{4}{3} - 4 \sqrt{3}$$
$$x_{1} = \frac{4}{3} - 4 \sqrt{3}$$
This roots
$$x_{1} = \frac{4}{3} - 4 \sqrt{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$\left(\frac{4}{3} - 4 \sqrt{3}\right) + - \frac{1}{10}$$
=
$$\frac{37}{30} - 4 \sqrt{3}$$
substitute to the expression
$$- \frac{x}{4} + \frac{1}{3} > \sqrt{3}$$
$$\frac{1}{3} - \frac{\frac{37}{30} - 4 \sqrt{3}}{4} > \sqrt{3}$$
1 ___ ___ -- + \/ 3 > \/ 3 40
the solution of our inequality is:
$$x < \frac{4}{3} - 4 \sqrt{3}$$
_____
\
-------ο-------
x1
Solving inequality on a graph
Rapid solution 2
[src]
4 ___
(-oo, - - 4*\/ 3 )
3
$$x\ in\ \left(-\infty, \frac{4}{3} - 4 \sqrt{3}\right)$$
x in Interval.open(-oo, 4/3 - 4*sqrt(3))
Rapid solution
[src]
/ 4 ___\ And|-oo < x, x < - - 4*\/ 3 | \ 3 /
$$-\infty < x \wedge x < \frac{4}{3} - 4 \sqrt{3}$$
(-oo < x)∧(x < 4/3 - 4*sqrt(3))