Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- 9x+8<8x-8
-
sin2x>sqrt2/2
- sqrt(x)+6>sqrt(x)+7+sqrt(2*x)-5
- (a-3)*x^2-2*a*x+3-6>0
- Canonical form:
- =0
-
Identical expressions
- (two x^2-11x+ five)/(log1 three (x+3))<= zero
- (2x squared minus 11x plus 5) divide by ( logarithm of 13(x plus 3)) less than or equal to 0
- (two x squared minus 11x plus five) divide by ( logarithm of 1 three (x plus 3)) less than or equal to zero
- (2x2-11x+5)/(log13(x+3))<=0
- 2x2-11x+5/log13x+3<=0
- (2x²-11x+5)/(log13(x+3))<=0
- (2x to the power of 2-11x+5)/(log13(x+3))<=0
- 2x^2-11x+5/log13x+3<=0
- (2x^2-11x+5)/(log13(x+3))<=O
- (2x^2-11x+5) divide by (log13(x+3))<=0
-
Similar expressions
- (2x^2-11x+5)/(log13(x-3))<=0
- (2x^2-11x-5)/(log13(x+3))<=0
- (2x^2+11x+5)/(log13(x+3))<=0
(2x^2-11x+5)/(log13(x+3))<=0 inequation
The solution
You have entered
[src]
2 2*x - 11*x + 5 --------------- <= 0 /log(x + 3)\ |----------| \ log(13) /
$$\frac{\left(2 x^{2} - 11 x\right) + 5}{\frac{1}{\log{\left(13 \right)}} \log{\left(x + 3 \right)}} \leq 0$$
(2*x^2 - 11*x + 5)/((log(x + 3)/log(13))) <= 0
Detail solution
Given the inequality:
$$\frac{\left(2 x^{2} - 11 x\right) + 5}{\frac{1}{\log{\left(13 \right)}} \log{\left(x + 3 \right)}} \leq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\left(2 x^{2} - 11 x\right) + 5}{\frac{1}{\log{\left(13 \right)}} \log{\left(x + 3 \right)}} = 0$$
Solve:
$$x_{1} = \frac{1}{2}$$
$$x_{2} = 5$$
$$x_{1} = \frac{1}{2}$$
$$x_{2} = 5$$
This roots
$$x_{1} = \frac{1}{2}$$
$$x_{2} = 5$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{1}{2}$$
=
$$\frac{2}{5}$$
substitute to the expression
$$\frac{\left(2 x^{2} - 11 x\right) + 5}{\frac{1}{\log{\left(13 \right)}} \log{\left(x + 3 \right)}} \leq 0$$
$$\frac{\left(- \frac{2 \cdot 11}{5} + 2 \left(\frac{2}{5}\right)^{2}\right) + 5}{\frac{1}{\log{\left(13 \right)}} \log{\left(\frac{2}{5} + 3 \right)}} \leq 0$$
but
Then
$$x \leq \frac{1}{2}$$
no execute
one of the solutions of our inequality is:
$$x \geq \frac{1}{2} \wedge x \leq 5$$
$$\frac{\left(2 x^{2} - 11 x\right) + 5}{\frac{1}{\log{\left(13 \right)}} \log{\left(x + 3 \right)}} \leq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\left(2 x^{2} - 11 x\right) + 5}{\frac{1}{\log{\left(13 \right)}} \log{\left(x + 3 \right)}} = 0$$
Solve:
$$x_{1} = \frac{1}{2}$$
$$x_{2} = 5$$
$$x_{1} = \frac{1}{2}$$
$$x_{2} = 5$$
This roots
$$x_{1} = \frac{1}{2}$$
$$x_{2} = 5$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{1}{2}$$
=
$$\frac{2}{5}$$
substitute to the expression
$$\frac{\left(2 x^{2} - 11 x\right) + 5}{\frac{1}{\log{\left(13 \right)}} \log{\left(x + 3 \right)}} \leq 0$$
$$\frac{\left(- \frac{2 \cdot 11}{5} + 2 \left(\frac{2}{5}\right)^{2}\right) + 5}{\frac{1}{\log{\left(13 \right)}} \log{\left(\frac{2}{5} + 3 \right)}} \leq 0$$
23*log(13) ------------ <= 0 25*log(17/5)
but
23*log(13) ------------ >= 0 25*log(17/5)
Then
$$x \leq \frac{1}{2}$$
no execute
one of the solutions of our inequality is:
$$x \geq \frac{1}{2} \wedge x \leq 5$$
_____
/ \
-------•-------•-------
x1 x2
Rapid solution
[src]
Or(And(-3 <= x, x < -2), And(1/2 <= x, x <= 5))
$$\left(-3 \leq x \wedge x < -2\right) \vee \left(\frac{1}{2} \leq x \wedge x \leq 5\right)$$
((-3 <= x)∧(x < -2))∨((1/2 <= x)∧(x <= 5))
Rapid solution 2
[src]
[-3, -2) U [1/2, 5]
$$x\ in\ \left[-3, -2\right) \cup \left[\frac{1}{2}, 5\right]$$
x in Union(Interval.Ropen(-3, -2), Interval(1/2, 5))