Mister Exam

Other calculators

  • 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

  • one / two *(one / two)^ two x- one -(one /2)^x- one > zero
  • 1 divide by 2 multiply by (1 divide by 2) squared x minus 1 minus (1 divide by 2) to the power of x minus 1 greater than 0
  • one divide by two multiply by (one divide by two) to the power of two x minus one minus (one divide by 2) to the power of x minus one greater than zero
  • 1/2*(1/2)2x-1-(1/2)x-1>0
  • 1/2*1/22x-1-1/2x-1>0
  • 1/2*(1/2)²x-1-(1/2)^x-1>0
  • 1/2*(1/2) to the power of 2x-1-(1/2) to the power of x-1>0
  • 1/2(1/2)^2x-1-(1/2)^x-1>0
  • 1/2(1/2)2x-1-(1/2)x-1>0
  • 1/21/22x-1-1/2x-1>0
  • 1/21/2^2x-1-1/2^x-1>0
  • 1 divide by 2*(1 divide by 2)^2x-1-(1 divide by 2)^x-1>0

  • Similar expressions

  • 1/2*(1/2)^2x-1+(1/2)^x-1>0
  • 1/2*(1/2)^2x-1-(1/2)^x+1>0
  • 1/2*(1/2)^2x+1-(1/2)^x-1>0
Solving inequalities/ 1/2*(1/2)^2x-1-(1/2)^x-1>0

1/2*(1/2)^2x-1-(1/2)^x-1>0 inequation

A inequation with variable

The solution

You have entered [src] 
/1 \                    
|--|                    
| 2|                    
\2 /          -x        
----*x - 1 - 2   - 1 > 0
 2
$$\left(\left(\frac{1}{2 \cdot 4} x - 1\right) - \left(\frac{1}{2}\right)^{x}\right) - 1 > 0$$ 
((1/2)^2/2)*x - 1 - (1/2)^x - 1 > 0
Detail solution
Given the inequality:
$$\left(\left(\frac{1}{2 \cdot 4} x - 1\right) - \left(\frac{1}{2}\right)^{x}\right) - 1 > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(\left(\frac{1}{2 \cdot 4} x - 1\right) - \left(\frac{1}{2}\right)^{x}\right) - 1 = 0$$
Solve:
$$x_{1} = \frac{W\left(\frac{\log{\left(2 \right)}}{8192}\right)}{\log{\left(2 \right)}} + 16$$
$$x_{1} = \frac{W\left(\frac{\log{\left(2 \right)}}{8192}\right)}{\log{\left(2 \right)}} + 16$$
This roots
$$x_{1} = \frac{W\left(\frac{\log{\left(2 \right)}}{8192}\right)}{\log{\left(2 \right)}} + 16$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \left(\frac{W\left(\frac{\log{\left(2 \right)}}{8192}\right)}{\log{\left(2 \right)}} + 16\right)$$
=
$$\frac{W\left(\frac{\log{\left(2 \right)}}{8192}\right)}{\log{\left(2 \right)}} + \frac{159}{10}$$
substitute to the expression
$$\left(\left(\frac{1}{2 \cdot 4} x - 1\right) - \left(\frac{1}{2}\right)^{x}\right) - 1 > 0$$
$$-1 + \left(- \left(\frac{1}{2}\right)^{\frac{W\left(\frac{\log{\left(2 \right)}}{8192}\right)}{\log{\left(2 \right)}} + \frac{159}{10}} + \left(-1 + \frac{\left(\frac{1}{2}\right)^{2}}{2} \left(\frac{W\left(\frac{\log{\left(2 \right)}}{8192}\right)}{\log{\left(2 \right)}} + \frac{159}{10}\right)\right)\right) > 0$$
                 /log(2)\                
                W|------|                
          159    \ 8192 /    /log(2)\    
        - --- - ---------   W|------| > 0
  1        10     log(2)     \ 8192 /    
- -- - 2                  + ---------    
  80                         8*log(2)

Then
$$x < \frac{W\left(\frac{\log{\left(2 \right)}}{8192}\right)}{\log{\left(2 \right)}} + 16$$
no execute
the solution of our inequality is:
$$x > \frac{W\left(\frac{\log{\left(2 \right)}}{8192}\right)}{\log{\left(2 \right)}} + 16$$
         _____  
        /
-------ο-------
       x1
Solving inequality on a graph
    © Mister Exam – Calculator