Mister Exam
(2,5-√6)(10-4x)>0 inequation
The solution
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/5 ___\ |- - \/ 6 |*(10 - 4*x) > 0 \2 /
$$\left(\frac{5}{2} - \sqrt{6}\right) \left(10 - 4 x\right) > 0$$
(5/2 - sqrt(6))*(10 - 4*x) > 0
Detail solution
Given the inequality:
$$\left(\frac{5}{2} - \sqrt{6}\right) \left(10 - 4 x\right) > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(\frac{5}{2} - \sqrt{6}\right) \left(10 - 4 x\right) = 0$$
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:
$$- 10 x + 4 \sqrt{6} x - 10 \sqrt{6} = -25$$
Divide both parts of the equation by (-10*x - 10*sqrt(6) + 4*x*sqrt(6))/x
We get the answer: x = 5/2
$$x_{1} = \frac{5}{2}$$
$$x_{1} = \frac{5}{2}$$
This roots
$$x_{1} = \frac{5}{2}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{5}{2}$$
=
$$\frac{12}{5}$$
substitute to the expression
$$\left(\frac{5}{2} - \sqrt{6}\right) \left(10 - 4 x\right) > 0$$
$$\left(\frac{5}{2} - \sqrt{6}\right) \left(10 - \frac{4 \cdot 12}{5}\right) > 0$$
the solution of our inequality is:
$$x < \frac{5}{2}$$
$$\left(\frac{5}{2} - \sqrt{6}\right) \left(10 - 4 x\right) > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(\frac{5}{2} - \sqrt{6}\right) \left(10 - 4 x\right) = 0$$
Solve:
Given the equation:
((5/2)-sqrt(6))*(10-4*x) = 0
Expand expressions:
25 - 10*x - 10*sqrt(6) + 4*x*sqrt(6) = 0
Reducing, you get:
25 - 10*x - 10*sqrt(6) + 4*x*sqrt(6) = 0
Expand brackets in the left part
25 - 10*x - 10*sqrt6 + 4*x*sqrt6 = 0
Move free summands (without x)
from left part to right part, we given:
$$- 10 x + 4 \sqrt{6} x - 10 \sqrt{6} = -25$$
Divide both parts of the equation by (-10*x - 10*sqrt(6) + 4*x*sqrt(6))/x
x = -25 / ((-10*x - 10*sqrt(6) + 4*x*sqrt(6))/x)
We get the answer: x = 5/2
$$x_{1} = \frac{5}{2}$$
$$x_{1} = \frac{5}{2}$$
This roots
$$x_{1} = \frac{5}{2}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{5}{2}$$
=
$$\frac{12}{5}$$
substitute to the expression
$$\left(\frac{5}{2} - \sqrt{6}\right) \left(10 - 4 x\right) > 0$$
$$\left(\frac{5}{2} - \sqrt{6}\right) \left(10 - \frac{4 \cdot 12}{5}\right) > 0$$
___
2*\/ 6
1 - ------- > 0
5
the solution of our inequality is:
$$x < \frac{5}{2}$$
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x1
Solving inequality on a graph
Rapid solution
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And(-oo < x, x < 5/2)
$$-\infty < x \wedge x < \frac{5}{2}$$
(-oo < x)∧(x < 5/2)
Rapid solution 2
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(-oo, 5/2)
$$x\ in\ \left(-\infty, \frac{5}{2}\right)$$
x in Interval.open(-oo, 5/2)