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How to use it?
- Inequation:
- 2x-1:5-x>_0
- 6+12x≤0
- (1/4)*(2^(x^2+x))^(1/6)>=1
- 2x^2-5x^2+2>=0
- Sum of series:
-
0,1
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Identical expressions
- (two x- one)/(x+ two)-2< zero , one
- (2x minus 1) divide by (x plus 2) minus 2 less than 0,1
- (two x minus one) divide by (x plus two) minus 2 less than zero , one
- 2x-1/x+2-2<0,1
- (2x-1) divide by (x+2)-2<0,1
-
Similar expressions
- (2x+1)/(x+2)-2<0,1
- (2x-1)/(x-2)-2<0,1
- ((2x-1)/(x+2))-2<0,001
- (2x-1)/(x+2)+2<0,1
(2x-1)/(x+2)-2<0,1 inequation
The solution
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[src]
2*x - 1 ------- - 2 < 1/10 x + 2
$$-2 + \frac{2 x - 1}{x + 2} < \frac{1}{10}$$
-2 + (2*x - 1)/(x + 2) < 1/10
Detail solution
Given the inequality:
$$-2 + \frac{2 x - 1}{x + 2} < \frac{1}{10}$$
To solve this inequality, we must first solve the corresponding equation:
$$-2 + \frac{2 x - 1}{x + 2} = \frac{1}{10}$$
Solve:
Given the equation:
$$-2 + \frac{2 x - 1}{x + 2} = \frac{1}{10}$$
Multiply the equation sides by the denominator 2 + x
we get:
$$-5 = \frac{x}{10} + \frac{1}{5}$$
Move free summands (without x)
from left part to right part, we given:
$$0 = \frac{x}{10} + \frac{26}{5}$$
Move the summands with the unknown x
from the right part to the left part:
$$\frac{\left(-1\right) x}{10} = \frac{26}{5}$$
Divide both parts of the equation by -1/10
$$x_{1} = -52$$
$$x_{1} = -52$$
This roots
$$x_{1} = -52$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-52 + - \frac{1}{10}$$
=
$$- \frac{521}{10}$$
substitute to the expression
$$-2 + \frac{2 x - 1}{x + 2} < \frac{1}{10}$$
$$-2 + \frac{\frac{\left(-521\right) 2}{10} - 1}{- \frac{521}{10} + 2} < \frac{1}{10}$$
the solution of our inequality is:
$$x < -52$$
$$-2 + \frac{2 x - 1}{x + 2} < \frac{1}{10}$$
To solve this inequality, we must first solve the corresponding equation:
$$-2 + \frac{2 x - 1}{x + 2} = \frac{1}{10}$$
Solve:
Given the equation:
$$-2 + \frac{2 x - 1}{x + 2} = \frac{1}{10}$$
Multiply the equation sides by the denominator 2 + x
we get:
$$-5 = \frac{x}{10} + \frac{1}{5}$$
Move free summands (without x)
from left part to right part, we given:
$$0 = \frac{x}{10} + \frac{26}{5}$$
Move the summands with the unknown x
from the right part to the left part:
$$\frac{\left(-1\right) x}{10} = \frac{26}{5}$$
Divide both parts of the equation by -1/10
x = 26/5 / (-1/10)
$$x_{1} = -52$$
$$x_{1} = -52$$
This roots
$$x_{1} = -52$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-52 + - \frac{1}{10}$$
=
$$- \frac{521}{10}$$
substitute to the expression
$$-2 + \frac{2 x - 1}{x + 2} < \frac{1}{10}$$
$$-2 + \frac{\frac{\left(-521\right) 2}{10} - 1}{- \frac{521}{10} + 2} < \frac{1}{10}$$
50 --- < 1/10 501
the solution of our inequality is:
$$x < -52$$
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Solving inequality on a graph
Rapid solution 2
[src]
(-oo, -52) U (-2, oo)
$$x\ in\ \left(-\infty, -52\right) \cup \left(-2, \infty\right)$$
x in Union(Interval.open(-oo, -52), Interval.open(-2, oo))
Rapid solution
[src]
Or(And(-oo < x, x < -52), And(-2 < x, x < oo))
$$\left(-\infty < x \wedge x < -52\right) \vee \left(-2 < x \wedge x < \infty\right)$$
((-oo < x)∧(x < -52))∨((-2 < x)∧(x < oo))