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How do you solve these? For some reason the answers I get with these look so wrong to me. 

 Jun 7, 2019

Best Answer 

 #1
avatar+8829 
+4
a.__ -4x6  =  -2916 ___ Divide both sides of the equation by  -4
  x6  =  729

 

 

Take the ± 6th root of both sides
  x  =  \(\pm\sqrt[6]{729}\)   Plug this into a calculator or note that  36  =  729  so we can rewrite  729  as  36
  x  =  \(\pm\sqrt[6]{3^6}\)

 

 

Simplify
  x  =  ± 3    

 

 

 

This equation has two solutions. There are two values of  x  which make the equation true.

They are:  x = 3   and   x = -3

       

b.

93 - 7x3  =  23   Subtract  93  from both sides of the equation.
  -7x3  =  -70

 

 

Divide both sides of the equation by  -7
  x3  =  10   Take the cube root of both sides.
  x  =  \(\sqrt[3]{10}\)

 

 

To get an approximate solution, plug  \(\sqrt[3]{10}\)  into a calculator.
  x  ≈  2.154    

 

 

     
c. (-5p)5  =  -65   Take the fifth root of both sides.
  -5p  =  \(\sqrt[5]{-65}\)

 

 

Divide both sides by  -5
  p  =  \(\frac{\sqrt[5]{-65}}{-5}\)   SImplify
  p  =  \(\frac{\sqrt[5]{-1}\,\cdot\,\sqrt[5]{65}}{-5}\)

 

 

 
  p  =  \(\frac{-1\ \cdot\ \sqrt[5]{65}}{-5}\)    
  p  =  \(\frac{\sqrt[5]{65}}{5}\)

 

 

 
  p  ≈  0.461    

 

 

     
d. \(-7+\frac{14}{x-3}\ =\ -5\)   Add  7  to both sides.
  \(\frac{14}{x-3}\ =\ 2\)

 

 

Multiply both sides by  (x - 3)  and note  x ≠ 3
  14  =  2(x - 3)   Divide both sides by  2
  7  =  x - 3

 

 

Add  3  to both sides
  10  =  x    
  x  =  10

 

 

 
 Jun 7, 2019
 #1
avatar+8829 
+4
Best Answer
a.__ -4x6  =  -2916 ___ Divide both sides of the equation by  -4
  x6  =  729

 

 

Take the ± 6th root of both sides
  x  =  \(\pm\sqrt[6]{729}\)   Plug this into a calculator or note that  36  =  729  so we can rewrite  729  as  36
  x  =  \(\pm\sqrt[6]{3^6}\)

 

 

Simplify
  x  =  ± 3    

 

 

 

This equation has two solutions. There are two values of  x  which make the equation true.

They are:  x = 3   and   x = -3

       

b.

93 - 7x3  =  23   Subtract  93  from both sides of the equation.
  -7x3  =  -70

 

 

Divide both sides of the equation by  -7
  x3  =  10   Take the cube root of both sides.
  x  =  \(\sqrt[3]{10}\)

 

 

To get an approximate solution, plug  \(\sqrt[3]{10}\)  into a calculator.
  x  ≈  2.154    

 

 

     
c. (-5p)5  =  -65   Take the fifth root of both sides.
  -5p  =  \(\sqrt[5]{-65}\)

 

 

Divide both sides by  -5
  p  =  \(\frac{\sqrt[5]{-65}}{-5}\)   SImplify
  p  =  \(\frac{\sqrt[5]{-1}\,\cdot\,\sqrt[5]{65}}{-5}\)

 

 

 
  p  =  \(\frac{-1\ \cdot\ \sqrt[5]{65}}{-5}\)    
  p  =  \(\frac{\sqrt[5]{65}}{5}\)

 

 

 
  p  ≈  0.461    

 

 

     
d. \(-7+\frac{14}{x-3}\ =\ -5\)   Add  7  to both sides.
  \(\frac{14}{x-3}\ =\ 2\)

 

 

Multiply both sides by  (x - 3)  and note  x ≠ 3
  14  =  2(x - 3)   Divide both sides by  2
  7  =  x - 3

 

 

Add  3  to both sides
  10  =  x    
  x  =  10

 

 

 
hectictar Jun 7, 2019

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