Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- (3^2x^2)+3^(x^2+2x+5)>10*3^4x+6
- 0x+4>10
- 4^x-1+2^x-2-3/2<=0
- x(1-x)≥0
- Derivative of:
-
-5
- -5
- Limit of the function:
-
-5
-
Identical expressions
- |x- one |-(six /|x- one |)<- five
- module of x minus 1| minus (6 divide by |x minus 1|) less than minus 5
- module of x minus one | minus (six divide by |x minus one |) less than minus five
- |x-1|-6/|x-1|<-5
- |x-1|-(6 divide by |x-1|)<-5
-
Similar expressions
- |x-1|-(6/|x-1|)<+5
- |x+1|-(6/|x-1|)<-5
- |x-1|+(6/|x-1|)<-5
- |x-1|-(6/|x+1|)<-5
|x-1|-(6/|x-1|)<-5 inequation
The solution
You have entered
[src]
6
|x - 1| - ------- < -5
|x - 1|
$$\left|{x - 1}\right| - \frac{6}{\left|{x - 1}\right|} < -5$$
|x - 1| - 6/|x - 1| < -5
Detail solution
Given the inequality:
$$\left|{x - 1}\right| - \frac{6}{\left|{x - 1}\right|} < -5$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{x - 1}\right| - \frac{6}{\left|{x - 1}\right|} = -5$$
Solve:
$$x_{1} = 0$$
$$x_{2} = 2$$
$$x_{1} = 0$$
$$x_{2} = 2$$
This roots
$$x_{1} = 0$$
$$x_{2} = 2$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 0$$
=
$$-0.1$$
substitute to the expression
$$\left|{x - 1}\right| - \frac{6}{\left|{x - 1}\right|} < -5$$
$$- \frac{6}{\left|{-1 - 0.1}\right|} + \left|{-1 - 0.1}\right| < -5$$
but
Then
$$x < 0$$
no execute
one of the solutions of our inequality is:
$$x > 0 \wedge x < 2$$
$$\left|{x - 1}\right| - \frac{6}{\left|{x - 1}\right|} < -5$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{x - 1}\right| - \frac{6}{\left|{x - 1}\right|} = -5$$
Solve:
$$x_{1} = 0$$
$$x_{2} = 2$$
$$x_{1} = 0$$
$$x_{2} = 2$$
This roots
$$x_{1} = 0$$
$$x_{2} = 2$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 0$$
=
$$-0.1$$
substitute to the expression
$$\left|{x - 1}\right| - \frac{6}{\left|{x - 1}\right|} < -5$$
$$- \frac{6}{\left|{-1 - 0.1}\right|} + \left|{-1 - 0.1}\right| < -5$$
-4.35454545454545 < -5
but
-4.35454545454545 > -5
Then
$$x < 0$$
no execute
one of the solutions of our inequality is:
$$x > 0 \wedge x < 2$$
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x1 x2
Solving inequality on a graph
Rapid solution
[src]
Or(And(0 < x, x < 1), And(1 < x, x < 2))
$$\left(0 < x \wedge x < 1\right) \vee \left(1 < x \wedge x < 2\right)$$
((0 < x)∧(x < 1))∨((1 < x)∧(x < 2))
Rapid solution 2
[src]
(0, 1) U (1, 2)
$$x\ in\ \left(0, 1\right) \cup \left(1, 2\right)$$
x in Union(Interval.open(0, 1), Interval.open(1, 2))