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  • Inequation:
  • xy>-4
  • (log(x^2+9)/log(3))*log((4/5))*(3*x)/(x+2)-log((4/5))*(6-x)<=0
  • (2^2-x)>2c-3
  • 1-x>3-2*x

  • Identical expressions

  • two ^ four *sqrt(x^ two - three)< two ^ four *sqrt(x+ three)
  • 2 to the power of 4 multiply by square root of (x squared minus 3) less than 2 to the power of 4 multiply by square root of (x plus 3)
  • two to the power of four multiply by square root of (x to the power of two minus three) less than two to the power of four multiply by square root of (x plus three)
  • 2^4*√(x^2-3)<2^4*√(x+3)
  • 24*sqrt(x2-3)<24*sqrt(x+3)
  • 24*sqrtx2-3<24*sqrtx+3
  • 2⁴*sqrt(x²-3)<2⁴*sqrt(x+3)
  • 2 to the power of 4*sqrt(x to the power of 2-3)<2 to the power of 4*sqrt(x+3)
  • 2^4sqrt(x^2-3)<2^4sqrt(x+3)
  • 24sqrt(x2-3)<24sqrt(x+3)
  • 24sqrtx2-3<24sqrtx+3
  • 2^4sqrtx^2-3<2^4sqrtx+3

  • Similar expressions

  • 2^4*sqrt(x^2+3)<2^4*sqrt(x+3)
  • 2^4*sqrt(x^2-3)<2^4*sqrt(x-3)
Solving inequalities/ 2^4*sqrt(x^2-3)<2^4*sqrt(x+3)

2^4*sqrt(x^2-3)<2^4*sqrt(x+3) inequation

A inequation with variable

The solution

You have entered [src] 
      ________               
 4   /  2         4   _______
2 *\/  x  - 3  < 2 *\/ x + 3
$$2^{4} \sqrt{x^{2} - 3} < 2^{4} \sqrt{x + 3}$$ 
2^4*sqrt(x^2 - 1*3) < 2^4*sqrt(x + 3)
Detail solution
Given the inequality:
$$2^{4} \sqrt{x^{2} - 3} < 2^{4} \sqrt{x + 3}$$
To solve this inequality, we must first solve the corresponding equation:
$$2^{4} \sqrt{x^{2} - 3} = 2^{4} \sqrt{x + 3}$$
Solve:
$$x_{1} = -2$$
$$x_{2} = 3$$
$$x_{1} = -2$$
$$x_{2} = 3$$
This roots
$$x_{1} = -2$$
$$x_{2} = 3$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-2 - \frac{1}{10}$$
=
$$- \frac{21}{10}$$
substitute to the expression
$$2^{4} \sqrt{x^{2} - 3} < 2^{4} \sqrt{x + 3}$$
$$2^{4} \sqrt{\left(-1\right) 3 + \left(- \frac{21}{10}\right)^{2}} < 2^{4} \sqrt{- \frac{21}{10} + 3}$$
    _____        ____
8*\/ 141    24*\/ 10 
--------- < ---------
    5           5

but
    _____        ____
8*\/ 141    24*\/ 10 
--------- > ---------
    5           5

Then
$$x < -2$$
no execute
one of the solutions of our inequality is:
$$x > -2 \wedge x < 3$$
         _____  
        /     \  
-------ο-------ο-------
       x_1      x_2
Solving inequality on a graph
Rapid solution [src] 
  /   /        ___        \     /  ___            \\
Or\And\x <= -\/ 3 , -2 < x/, And\\/ 3  <= x, x < 3//
$$\left(x \leq - \sqrt{3} \wedge -2 < x\right) \vee \left(\sqrt{3} \leq x \wedge x < 3\right)$$ 
((x < 3)∧(sqrt(3) <= x))∨((-2 < x)∧(x <= -sqrt(3)))
Rapid solution 2 [src] 
        ___       ___    
(-2, -\/ 3 ] U [\/ 3 , 3)
$$x\ in\ \left(-2, - \sqrt{3}\right] \cup \left[\sqrt{3}, 3\right)$$ 
x in Union(Interval.Lopen(-2, -sqrt(3)), Interval.Ropen(sqrt(3), 3))
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