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  • Identical expressions

  • (twenty-seven - three ^x)*(seven ^x- seven)/ five ^x≥ zero
  • (27 minus 3 to the power of x) multiply by (7 to the power of x minus 7) divide by 5 to the power of x≥0
  • (twenty minus seven minus three to the power of x) multiply by (seven to the power of x minus seven) divide by five to the power of x≥ zero
  • (27-3x)*(7x-7)/5x≥0
  • 27-3x*7x-7/5x≥0
  • (27-3^x)(7^x-7)/5^x≥0
  • (27-3x)(7x-7)/5x≥0
  • 27-3x7x-7/5x≥0
  • 27-3^x7^x-7/5^x≥0
  • (27-3^x)*(7^x-7) divide by 5^x≥0

  • Similar expressions

  • (27-3^x)*(7^x+7)/5^x≥0
  • (27+3^x)*(7^x-7)/5^x≥0
Solving inequalities/ (27-3^x)*(7^x-7)/5^x≥0

(27-3^x)*(7^x-7)/5^x≥0 inequation

A inequation with variable

The solution

You have entered [src] 
/      x\ / x    \     
\27 - 3 /*\7  - 7/     
------------------ >= 0
         x             
        5
$$\frac{\left(27 - 3^{x}\right) \left(7^{x} - 7\right)}{5^{x}} \geq 0$$ 
((27 - 3^x)*(7^x - 7))/5^x >= 0
Detail solution
Given the inequality:
$$\frac{\left(27 - 3^{x}\right) \left(7^{x} - 7\right)}{5^{x}} \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\left(27 - 3^{x}\right) \left(7^{x} - 7\right)}{5^{x}} = 0$$
Solve:
$$x_{1} = 1$$
$$x_{2} = 3$$
$$x_{1} = 1$$
$$x_{2} = 3$$
This roots
$$x_{1} = 1$$
$$x_{2} = 3$$
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
$$\frac{\left(27 - 3^{x}\right) \left(7^{x} - 7\right)}{5^{x}} \geq 0$$
$$\frac{\left(-7 + 7^{\frac{9}{10}}\right) \left(27 - 3^{\frac{9}{10}}\right)}{5^{\frac{9}{10}}} \geq 0$$
10___ /      9/10\ /      9/10\     
\/ 5 *\-7 + 7    /*\27 - 3    /     
------------------------------- >= 0
               5

but
10___ /      9/10\ /      9/10\    
\/ 5 *\-7 + 7    /*\27 - 3    /    
------------------------------- < 0
               5

Then
$$x \leq 1$$
no execute
one of the solutions of our inequality is:
$$x \geq 1 \wedge x \leq 3$$
         _____  
        /     \  
-------•-------•-------
       x1      x2
Solving inequality on a graph
Rapid solution [src] 
And(1 <= x, x <= 3)
$$1 \leq x \wedge x \leq 3$$ 
(1 <= x)∧(x <= 3)
Rapid solution 2 [src] 
[1, 3]
$$x\ in\ \left[1, 3\right]$$ 
x in Interval(1, 3)
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