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  • Inequation:
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  • 1,5^((x^2+x-20)/x)<=1,5^0
  • (x+1/2)-(1-5x/5)>x

  • Identical expressions

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  • 1,5 to the power of ((x squared plus x minus 20) divide by x) less than or equal to 1,5 to the power of 0
  • one , five to the power of ((x to the power of two plus x minus twenty) divide by x) less than or equal to one , five to the power of zero
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  • 1,5x2+x-20/x<=1,50
  • 1,5^((x²+x-20)/x)<=1,5^0
  • 1,5 to the power of ((x to the power of 2+x-20)/x)<=1,5 to the power of 0
  • 1,5^x^2+x-20/x<=1,5^0
  • 1,5^((x^2+x-20) divide by x)<=1,5^0

  • Similar expressions

  • 1,5^((x^2-x-20)/x)<=1,5^0
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Solving inequalities/ 1,5^((x^2+x-20)/x)<=1,5^0

1,5^((x^2+x-20)/x)<=1,5^0 inequation

A inequation with variable

The solution

You have entered [src] 
    2                 
   x  + x - 20        
   -----------        
        x            0
3/2            <= 3/2
$$\left(\frac{3}{2}\right)^{\frac{\left(x^{2} + x\right) - 20}{x}} \leq \left(\frac{3}{2}\right)^{0}$$ 
(3/2)^((x^2 + x - 20)/x) <= (3/2)^0
Detail solution
Given the inequality:
$$\left(\frac{3}{2}\right)^{\frac{\left(x^{2} + x\right) - 20}{x}} \leq \left(\frac{3}{2}\right)^{0}$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(\frac{3}{2}\right)^{\frac{\left(x^{2} + x\right) - 20}{x}} = \left(\frac{3}{2}\right)^{0}$$
Solve:
$$x_{1} = -5$$
$$x_{2} = 4$$
$$x_{1} = -5$$
$$x_{2} = 4$$
This roots
$$x_{1} = -5$$
$$x_{2} = 4$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-5 + - \frac{1}{10}$$
=
$$- \frac{51}{10}$$
substitute to the expression
$$\left(\frac{3}{2}\right)^{\frac{\left(x^{2} + x\right) - 20}{x}} \leq \left(\frac{3}{2}\right)^{0}$$
$$\left(\frac{3}{2}\right)^{\frac{-20 + \left(- \frac{51}{10} + \left(- \frac{51}{10}\right)^{2}\right)}{- \frac{51}{10}}} \leq \left(\frac{3}{2}\right)^{0}$$
  91  419     
 ---  ---     
 510  510     
2   *3    <= 1
---------     
    3

one of the solutions of our inequality is:
$$x \leq -5$$
 _____           _____          
      \         /
-------•-------•-------
       x1      x2

Other solutions will get with the changeover to the next point
etc.
The answer:
$$x \leq -5$$
$$x \geq 4$$
Rapid solution 2 [src] 
(-oo, -5] U (0, 4]
$$x\ in\ \left(-\infty, -5\right] \cup \left(0, 4\right]$$ 
x in Union(Interval(-oo, -5), Interval.Lopen(0, 4))
Rapid solution [src] 
Or(And(x <= -5, -oo < x), And(x <= 4, 0 < x))
$$\left(x \leq -5 \wedge -\infty < x\right) \vee \left(x \leq 4 \wedge 0 < x\right)$$ 
((x <= -5)∧(-oo < x))∨((x <= 4)∧(0 < x))
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