Mister Exam
1/(1-2*x)>0 inequation
The solution
Detail solution
Given the inequality:
$$\frac{1}{1 - 2 x} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{1}{1 - 2 x} = 0$$
Solve:
Given the equation:
$$\frac{1}{1 - 2 x} = 0$$
Multiply the equation sides by the denominator 1 - 2*x
we get:
$$- \frac{1 - 2 x}{2 x - 1} = 0$$
Expand brackets in the left part
Looking for similar summands in the left part:
Move free summands (without x)
from left part to right part, we given:
$$- \frac{1 - 2 x}{2 x - 1} + 1 = 1$$
This equation has no roots
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example
$$\frac{1}{1 - 0 \cdot 2} > 0$$
so the inequality is always executed
$$\frac{1}{1 - 2 x} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{1}{1 - 2 x} = 0$$
Solve:
Given the equation:
$$\frac{1}{1 - 2 x} = 0$$
Multiply the equation sides by the denominator 1 - 2*x
we get:
$$- \frac{1 - 2 x}{2 x - 1} = 0$$
Expand brackets in the left part
-1-2*x-1+2*x = 0
Looking for similar summands in the left part:
-(1 - 2*x)/(-1 + 2*x) = 0
Move free summands (without x)
from left part to right part, we given:
$$- \frac{1 - 2 x}{2 x - 1} + 1 = 1$$
This equation has no roots
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example
x0 = 0
$$\frac{1}{1 - 0 \cdot 2} > 0$$
1 > 0
so the inequality is always executed
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)