Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- 1/2*(1/2)^2x-1-(1/2)^x-1>0
- √(x^2-2x)>4-x
- (x+3)^2>(x−23)^2
- 9x^2-24x+16>0
-
Identical expressions
- cbrt(two +log1/ five *x)*((x- fifteen)*(x- twenty-seven))/(x- thirty)> zero
- cubic root of (2 plus logarithm of 1 divide by 5 multiply by x) multiply by ((x minus 15) multiply by (x minus 27)) divide by (x minus 30) greater than 0
- cubic root of (two plus logarithm of 1 divide by five multiply by x) multiply by ((x minus fifteen) multiply by (x minus twenty minus seven)) divide by (x minus thirty) greater than zero
- cbrt(2+log1/5x)((x-15)(x-27))/(x-30)>0
- cbrt2+log1/5xx-15x-27/x-30>0
- cbrt(2+log1 divide by 5*x)*((x-15)*(x-27)) divide by (x-30)>0
-
Similar expressions
- cbrt(2+log1/5*x)*((x-15)*(x+27))/(x-30)>0
- cbrt(2+log1/5*x)*((x-15)*(x-27))/(x+30)>0
- cbrt(2+log1/5*x)*((x+15)*(x-27))/(x-30)>0
- cbrt(2-log1/5*x)*((x-15)*(x-27))/(x-30)>0
-
What you mean?
- ((log(1) + 2)/((5*x)))^(1/3)*(x - 1*15)*(x - 1*27)/(x - 1*30) > 0
- ((log(1) + 2)*x/5)^(1/3)*(x - 1*15)*(x - 1*27)/(x - 1*30) > 0
- (2 + log(1)/((5*x)))^(1/3)*(x - 1*15)*(x - 1*27)/(x - 1*30) > 0
- (x - 1*15)*(x - 1*27)*(log(1)*x/5 + 2)^(1/3)/(x - 1*30) > 0
- (2 + log(1)/((5*x)))^(1/3)*(x - 1*15)*(x - 1*27)/(x - 1*30) > 0
- (x - 1*15)*(x - 1*27)*(log(1)*x/5 + 2)^(1/3)/(x - 1*30) > 0
- (x - 1*15)*(x - 1*27)*(log(1)*x/5 + 2)^(1/3)/(x - 1*30) > 0
cbrt(2+log1/5*x)*((x-15)*(x-27))/(x-30)>0 inequation
The solution
You have entered
[src]
______________
/ log(1)*x
3 / 2 + -------- *(x - 15)*(x - 27)
\/ 5
------------------------------------ > 0
x - 30
$$\frac{\left(x - 15\right) \left(x - 27\right) \sqrt[3]{\frac{x \log{\left(1 \right)}}{5} + 2}}{x - 30} > 0$$
(x - 1*15)*(x - 1*27)*(log(1)*x/5 + 2)^(1/3)/(x - 1*30) > 0
Detail solution
Given the inequality:
$$\frac{\left(x - 15\right) \left(x - 27\right) \sqrt[3]{\frac{x \log{\left(1 \right)}}{5} + 2}}{x - 30} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\left(x - 15\right) \left(x - 27\right) \sqrt[3]{\frac{x \log{\left(1 \right)}}{5} + 2}}{x - 30} = 0$$
Solve:
$$x_{1} = 15$$
$$x_{2} = 27$$
$$x_{1} = 15$$
$$x_{2} = 27$$
This roots
$$x_{1} = 15$$
$$x_{2} = 27$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 15$$
=
$$\frac{149}{10}$$
substitute to the expression
$$\frac{\left(x - 15\right) \left(x - 27\right) \sqrt[3]{\frac{x \log{\left(1 \right)}}{5} + 2}}{x - 30} > 0$$
$$\frac{\left(\left(-1\right) 15 + \frac{149}{10}\right) \left(\left(-1\right) 27 + \frac{149}{10}\right) \sqrt[3]{\log{\left(1 \right)} \frac{1}{5} \cdot \frac{149}{10} + 2}}{\left(-1\right) 30 + \frac{149}{10}} > 0$$
Then
$$x < 15$$
no execute
one of the solutions of our inequality is:
$$x > 15 \wedge x < 27$$
$$\frac{\left(x - 15\right) \left(x - 27\right) \sqrt[3]{\frac{x \log{\left(1 \right)}}{5} + 2}}{x - 30} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\left(x - 15\right) \left(x - 27\right) \sqrt[3]{\frac{x \log{\left(1 \right)}}{5} + 2}}{x - 30} = 0$$
Solve:
$$x_{1} = 15$$
$$x_{2} = 27$$
$$x_{1} = 15$$
$$x_{2} = 27$$
This roots
$$x_{1} = 15$$
$$x_{2} = 27$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 15$$
=
$$\frac{149}{10}$$
substitute to the expression
$$\frac{\left(x - 15\right) \left(x - 27\right) \sqrt[3]{\frac{x \log{\left(1 \right)}}{5} + 2}}{x - 30} > 0$$
$$\frac{\left(\left(-1\right) 15 + \frac{149}{10}\right) \left(\left(-1\right) 27 + \frac{149}{10}\right) \sqrt[3]{\log{\left(1 \right)} \frac{1}{5} \cdot \frac{149}{10} + 2}}{\left(-1\right) 30 + \frac{149}{10}} > 0$$
3 ___
-121*\/ 2
---------- > 0
1510
Then
$$x < 15$$
no execute
one of the solutions of our inequality is:
$$x > 15 \wedge x < 27$$
_____
/ \
-------ο-------ο-------
x_1 x_2
Solving inequality on a graph
Rapid solution
[src]
Or(And(15 < x, x < 27), And(30 < x, x < oo))
$$\left(15 < x \wedge x < 27\right) \vee \left(30 < x \wedge x < \infty\right)$$
((15 < x)∧(x < 27))∨((30 < x)∧(x < oo))
Rapid solution 2
[src]
(15, 27) U (30, oo)
$$x\ in\ \left(15, 27\right) \cup \left(30, \infty\right)$$
x in Union(Interval.open(15, 27), Interval.open(30, oo))
The graph