Mister Exam
sqrt((x+1)/(2x-1))<1 inequation
The solution
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[src]
_________ / x + 1 / ------- < 1 \/ 2*x - 1
$$\sqrt{\frac{x + 1}{2 x - 1}} < 1$$
sqrt((x + 1)/(2*x - 1)) < 1
Detail solution
Given the inequality:
$$\sqrt{\frac{x + 1}{2 x - 1}} < 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\sqrt{\frac{x + 1}{2 x - 1}} = 1$$
Solve:
$$x_{1} = 2$$
$$x_{1} = 2$$
This roots
$$x_{1} = 2$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 2$$
=
$$\frac{19}{10}$$
substitute to the expression
$$\sqrt{\frac{x + 1}{2 x - 1}} < 1$$
$$\sqrt{\frac{1 + \frac{19}{10}}{-1 + \frac{2 \cdot 19}{10}}} < 1$$
but
Then
$$x < 2$$
no execute
the solution of our inequality is:
$$x > 2$$
$$\sqrt{\frac{x + 1}{2 x - 1}} < 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\sqrt{\frac{x + 1}{2 x - 1}} = 1$$
Solve:
$$x_{1} = 2$$
$$x_{1} = 2$$
This roots
$$x_{1} = 2$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 2$$
=
$$\frac{19}{10}$$
substitute to the expression
$$\sqrt{\frac{x + 1}{2 x - 1}} < 1$$
$$\sqrt{\frac{1 + \frac{19}{10}}{-1 + \frac{2 \cdot 19}{10}}} < 1$$
_____
\/ 203
------- < 1
14
but
_____
\/ 203
------- > 1
14
Then
$$x < 2$$
no execute
the solution of our inequality is:
$$x > 2$$
_____
/
-------ο-------
x1
Solving inequality on a graph
Rapid solution
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Or(And(x <= -1, -oo < x), And(2 < x, x < oo))
$$\left(x \leq -1 \wedge -\infty < x\right) \vee \left(2 < x \wedge x < \infty\right)$$
((x <= -1)∧(-oo < x))∨((2 < x)∧(x < oo))
Rapid solution 2
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(-oo, -1] U (2, oo)
$$x\ in\ \left(-\infty, -1\right] \cup \left(2, \infty\right)$$
x in Union(Interval(-oo, -1), Interval.open(2, oo))