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(31-5*2^x)*1/(4^x-24*2^x+128)>=0,25

  • How to use it?

  • Inequation:
  • (31-5*2^x)*1/(4^x-24*2^x+128)>=0,25 (31-5*2^x)*1/(4^x-24*2^x+128)>=0,25
  • 6x^2+17<0 6x^2+17<0
  • ctgx>=sqrt(3)/3 ctgx>=sqrt(3)/3
  • sin(x)tg2x>0 sin(x)tg2x>0

  • Identical expressions

  • (thirty-one - five * two ^x)* one /(four ^x- twenty-four * two ^x+ one hundred and twenty-eight)>= zero , twenty-five
  • (31 minus 5 multiply by 2 to the power of x) multiply by 1 divide by (4 to the power of x minus 24 multiply by 2 to the power of x plus 128) greater than or equal to 0,25
  • (thirty minus one minus five multiply by two to the power of x) multiply by one divide by (four to the power of x minus twenty minus four multiply by two to the power of x plus one hundred and twenty minus eight) greater than or equal to zero , twenty minus five
  • (31-5*2x)*1/(4x-24*2x+128)>=0,25
  • 31-5*2x*1/4x-24*2x+128>=0,25
  • (31-52^x)1/(4^x-242^x+128)>=0,25
  • (31-52x)1/(4x-242x+128)>=0,25
  • 31-52x1/4x-242x+128>=0,25
  • 31-52^x1/4^x-242^x+128>=0,25
  • (31-5*2^x)*1/(4^x-24*2^x+128)>=O,25
  • (31-5*2^x)*1 divide by (4^x-24*2^x+128)>=0,25

  • Similar expressions

  • (31-5*2^x)*1/(4^x+24*2^x+128)>=0,25
  • (31+5*2^x)*1/(4^x-24*2^x+128)>=0,25
  • (31-5*2^x)*1/(4^x-24*2^x-128)>=0,25
Solving inequalities/ (31-5*2^x)*1/(4^x-24*2^x+128)>=0,25

(31-5*2^x)*1/(4^x-24*2^x+128)>=0,25 inequation

A inequation with variable

The solution

You have entered [src] 
/        x\          1               
\31 - 5*2 /*1*---------------- >= 1/4
               x       x             
              4  - 24*2  + 128
$$\left(- 5 \cdot 2^{x} + 31\right) 1 \cdot \frac{1}{- 24 \cdot 2^{x} + 4^{x} + 128} \geq \frac{1}{4}$$ 
31 - 5*2^x*1/(-24*2^x + 4^x + 128) >= 1/4
Detail solution
Given the inequality:
$$\left(- 5 \cdot 2^{x} + 31\right) 1 \cdot \frac{1}{- 24 \cdot 2^{x} + 4^{x} + 128} \geq \frac{1}{4}$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(- 5 \cdot 2^{x} + 31\right) 1 \cdot \frac{1}{- 24 \cdot 2^{x} + 4^{x} + 128} = \frac{1}{4}$$
Solve:
$$x_{1} = 1$$
$$x_{1} = 1$$
This roots
$$x_{1} = 1$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 1$$
=
$$\frac{9}{10}$$
substitute to the expression
$$\left(- 5 \cdot 2^{x} + 31\right) 1 \cdot \frac{1}{- 24 \cdot 2^{x} + 4^{x} + 128} \geq \frac{1}{4}$$
$$\left(- 5 \cdot 2^{\frac{9}{10}} + 31\right) 1 \cdot \frac{1}{- 24 \cdot 2^{\frac{9}{10}} + 4^{\frac{9}{10}} + 128} \geq \frac{1}{4}$$
              9/10            
      31 - 5*2                
----------------------- >= 1/4
          9/10      4/5       
128 - 24*2     + 2*2

but
              9/10           
      31 - 5*2               
----------------------- < 1/4
          9/10      4/5      
128 - 24*2     + 2*2

Then
$$x \leq 1$$
no execute
the solution of our inequality is:
$$x \geq 1$$
         _____  
        /
-------•-------
       x_1
Solving inequality on a graph
Rapid solution [src] 
Or(And(3 < x, x < 4), x = 1)
$$\left(3 < x \wedge x < 4\right) \vee x = 1$$ 
(x = 1))∨((3 < x)∧(x < 4)
Rapid solution 2 [src] 
{1} U (3, 4)
$$x\ in\ \left\{1\right\} \cup \left(3, 4\right)$$ 
x in Union({1}, Interval.open(3, 4))
The graph
(31-5*2^x)*1/(4^x-24*2^x+128)>=0,25 inequation
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