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How to use it?
- Inequation:
- |0,5x+1|<=0
- -6*x^2+13*x-5>=0
- |x-1|-(6/|x-1|)<1
-
64/(2^(x+3))<=0,125^x-7
-
Identical expressions
- |x- one |-(six /|x- one |)< one
- module of x minus 1| minus (6 divide by |x minus 1|) less than 1
- module of x minus one | minus (six divide by |x minus one |) less than one
- |x-1|-6/|x-1|<1
- |x-1|-(6 divide by |x-1|)<1
-
Similar expressions
- |x+1|-(6/|x-1|)<1
- |x-1|-(6/(|x-1|))<-1
- |x-1|+(6/|x-1|)<1
- |x-1|-(6/|x+1|)<1
|x-1|-(6/|x-1|)<1 inequation
The solution
You have entered
[src]
6
|x - 1| - ------- < 1
|x - 1|
$$\left|{x - 1}\right| - \frac{6}{\left|{x - 1}\right|} < 1$$
|x - 1| - 6/|x - 1| < 1
Detail solution
Given the inequality:
$$\left|{x - 1}\right| - \frac{6}{\left|{x - 1}\right|} < 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{x - 1}\right| - \frac{6}{\left|{x - 1}\right|} = 1$$
Solve:
$$x_{1} = -2$$
$$x_{2} = 4$$
$$x_{1} = -2$$
$$x_{2} = 4$$
This roots
$$x_{1} = -2$$
$$x_{2} = 4$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-2 + - \frac{1}{10}$$
=
$$-2.1$$
substitute to the expression
$$\left|{x - 1}\right| - \frac{6}{\left|{x - 1}\right|} < 1$$
$$- \frac{6}{\left|{-2.1 - 1}\right|} + \left|{-2.1 - 1}\right| < 1$$
but
Then
$$x < -2$$
no execute
one of the solutions of our inequality is:
$$x > -2 \wedge x < 4$$
$$\left|{x - 1}\right| - \frac{6}{\left|{x - 1}\right|} < 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{x - 1}\right| - \frac{6}{\left|{x - 1}\right|} = 1$$
Solve:
$$x_{1} = -2$$
$$x_{2} = 4$$
$$x_{1} = -2$$
$$x_{2} = 4$$
This roots
$$x_{1} = -2$$
$$x_{2} = 4$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-2 + - \frac{1}{10}$$
=
$$-2.1$$
substitute to the expression
$$\left|{x - 1}\right| - \frac{6}{\left|{x - 1}\right|} < 1$$
$$- \frac{6}{\left|{-2.1 - 1}\right|} + \left|{-2.1 - 1}\right| < 1$$
1.16451612903226 < 1
but
1.16451612903226 > 1
Then
$$x < -2$$
no execute
one of the solutions of our inequality is:
$$x > -2 \wedge x < 4$$
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x1 x2
Solving inequality on a graph
Rapid solution
[src]
Or(And(-2 < x, x < 1), And(1 < x, x < 4))
$$\left(-2 < x \wedge x < 1\right) \vee \left(1 < x \wedge x < 4\right)$$
((-2 < x)∧(x < 1))∨((1 < x)∧(x < 4))
Rapid solution 2
[src]
(-2, 1) U (1, 4)
$$x\ in\ \left(-2, 1\right) \cup \left(1, 4\right)$$
x in Union(Interval.open(-2, 1), Interval.open(1, 4))