Mister Exam
(2,5-√6)*(11-4x)>0 inequation
The solution
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/5 ___\ |- - \/ 6 |*(11 - 4*x) > 0 \2 /
$$\left(\frac{5}{2} - \sqrt{6}\right) \left(11 - 4 x\right) > 0$$
(5/2 - sqrt(6))*(11 - 4*x) > 0
Detail solution
Given the inequality:
$$\left(\frac{5}{2} - \sqrt{6}\right) \left(11 - 4 x\right) > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(\frac{5}{2} - \sqrt{6}\right) \left(11 - 4 x\right) = 0$$
Solve:
Given the equation:
Expand expressions:
Reducing, you get:
Expand brackets in the left part
Move free summands (without x)
from left part to right part, we given:
$$- 10 x + 4 \sqrt{6} x - 11 \sqrt{6} = - \frac{55}{2}$$
Divide both parts of the equation by (-11*sqrt(6) - 10*x + 4*x*sqrt(6))/x
We get the answer: x = 11/4
$$x_{1} = \frac{11}{4}$$
$$x_{1} = \frac{11}{4}$$
This roots
$$x_{1} = \frac{11}{4}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{11}{4}$$
=
$$\frac{53}{20}$$
substitute to the expression
$$\left(\frac{5}{2} - \sqrt{6}\right) \left(11 - 4 x\right) > 0$$
$$\left(\frac{5}{2} - \sqrt{6}\right) \left(11 - \frac{4 \cdot 53}{20}\right) > 0$$
the solution of our inequality is:
$$x < \frac{11}{4}$$
$$\left(\frac{5}{2} - \sqrt{6}\right) \left(11 - 4 x\right) > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(\frac{5}{2} - \sqrt{6}\right) \left(11 - 4 x\right) = 0$$
Solve:
Given the equation:
((5/2)-sqrt(6))*(11-4*x) = 0
Expand expressions:
55/2 - 11*sqrt(6) - 10*x + 4*x*sqrt(6) = 0
Reducing, you get:
55/2 - 11*sqrt(6) - 10*x + 4*x*sqrt(6) = 0
Expand brackets in the left part
55/2 - 11*sqrt6 - 10*x + 4*x*sqrt6 = 0
Move free summands (without x)
from left part to right part, we given:
$$- 10 x + 4 \sqrt{6} x - 11 \sqrt{6} = - \frac{55}{2}$$
Divide both parts of the equation by (-11*sqrt(6) - 10*x + 4*x*sqrt(6))/x
x = -55/2 / ((-11*sqrt(6) - 10*x + 4*x*sqrt(6))/x)
We get the answer: x = 11/4
$$x_{1} = \frac{11}{4}$$
$$x_{1} = \frac{11}{4}$$
This roots
$$x_{1} = \frac{11}{4}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{11}{4}$$
=
$$\frac{53}{20}$$
substitute to the expression
$$\left(\frac{5}{2} - \sqrt{6}\right) \left(11 - 4 x\right) > 0$$
$$\left(\frac{5}{2} - \sqrt{6}\right) \left(11 - \frac{4 \cdot 53}{20}\right) > 0$$
___
2*\/ 6
1 - ------- > 0
5
the solution of our inequality is:
$$x < \frac{11}{4}$$
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Solving inequality on a graph
Rapid solution 2
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(-oo, 11/4)
$$x\ in\ \left(-\infty, \frac{11}{4}\right)$$
x in Interval.open(-oo, 11/4)
Rapid solution
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And(-oo < x, x < 11/4)
$$-\infty < x \wedge x < \frac{11}{4}$$
(-oo < x)∧(x < 11/4)