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  • Inequation:
  • 8x<=-3(1-x^2)
  • 0,5*(4^x+6)>1
  • -5/(x-2)^2<0
  • (3-7)^2>=(7-3)^2
  • Sum of series:
  • 1/3 1/3
  • Derivative of:
  • 1/3 1/3
  • Limit of the function:
  • 1/3

  • Identical expressions

  • one / sixteen ^ nine -x< one / three
  • 1 divide by 16 to the power of 9 minus x less than 1 divide by 3
  • one divide by sixteen to the power of nine minus x less than one divide by three
  • 1/169-x<1/3
  • 1/16⁹-x<1/3
  • 1 divide by 16^9-x<1 divide by 3

  • Similar expressions

  • 1/16^9+x<1/3
Solving inequalities/ 1/16^9-x<1/3

1/16^9-x<1/3 inequation

A inequation with variable

The solution

You have entered [src] 
 1           
--- - x < 1/3
  9          
16
$$- x + \left(\frac{1}{16}\right)^{9} < \frac{1}{3}$$ 
-x + (1/16)^9 < 1/3
Detail solution
Given the inequality:
$$- x + \left(\frac{1}{16}\right)^{9} < \frac{1}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$- x + \left(\frac{1}{16}\right)^{9} = \frac{1}{3}$$
Solve:
Given the linear equation:
1/16^9-x = 1/3

Move free summands (without x)
from left part to right part, we given:
$$- x = \frac{68719476733}{206158430208}$$
Divide both parts of the equation by -1
x = 68719476733/206158430208 / (-1)

$$x_{1} = - \frac{68719476733}{206158430208}$$
$$x_{1} = - \frac{68719476733}{206158430208}$$
This roots
$$x_{1} = - \frac{68719476733}{206158430208}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{68719476733}{206158430208} + - \frac{1}{10}$$
=
$$- \frac{446676598769}{1030792151040}$$
substitute to the expression
$$- x + \left(\frac{1}{16}\right)^{9} < \frac{1}{3}$$
$$\left(\frac{1}{16}\right)^{9} - - \frac{446676598769}{1030792151040} < \frac{1}{3}$$
13      
-- < 1/3
30

but
13      
-- > 1/3
30

Then
$$x < - \frac{68719476733}{206158430208}$$
no execute
the solution of our inequality is:
$$x > - \frac{68719476733}{206158430208}$$
         _____  
        /
-------ο-------
       x1
Solving inequality on a graph
Rapid solution [src] 
   /-68719476733             \
And|------------- < x, x < oo|
   \ 206158430208            /
$$- \frac{68719476733}{206158430208} < x \wedge x < \infty$$ 
(-68719476733/206158430208 < x)∧(x < oo)
Rapid solution 2 [src] 
 -68719476733      
(-------------, oo)
  206158430208
$$x\ in\ \left(- \frac{68719476733}{206158430208}, \infty\right)$$ 
x in Interval.open(-68719476733/206158430208, oo)
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