This question is pertaining to college algebra

Question

Solve for x:

 

5x= (2x-2)(m+6)

Answer 1

5x=(2x-2)(m+6)

5x=2xm-2m+12x-12

5x-2xm-12x=-2m-12

x(5-2m-12)=-2m-12

x(-7-2m)=-2m-12

x=(-2m-12)/(-7-2m)

x=(2m+12)/(7+2m)

Answer 2

5x= (2x-2)(m+6)

 

divide both sides by (m+6)

 

5x/(m+6) = 2x-2

 

divide both sides by 5x

 

1/(m+6) = (2x-2)/5x

 

factor out a 2

 

1/(m+6) = 2(x-1)/5x

 

multiply both sides by 5 and divide by 2

 

5/2(m+6) = (x-1)/x

 

5/2(m+6) = x/x - 1/x

 

5/2(m+6) = 1 - 1/x

 

subtract 1 from both sides

 

5/2(m+6) -1 = -1/x

combine into one fraction

 

5/2(m+6) - 2(m+6)/2(m+6) = -1/x

 

(5-2m -12)/(2m+12) = -1/x 

 

(7-2m)/(2m+12) = -1/x

 

now flip both fractions over and switch the negative sign

 

- (2m+12)/(7-2m) = x