8(b-x)=6b+ax solve for x

Question

I need help to solve for x in the equation 8(b-x)=6b+ax

Answer 1

8(b-x)=6b+ax

 

First, distribute (multiply) the 8 across the terms in parentheses:

 

8b - 8x = 6b + ax

 

Now we want to get the x's on one side of the equation, so add 8x to both sides:

 

8b - 8x + 8x = 6b + ax + 8x

 

8b = 6b + ax + 8x

 

Subtract 6b from both sides:

 

8b - 6b = ax + 8x + 6b - 6b

 

2b = ax + 8x

 

Factor out an x:

 

2b = (a+8)x

 

Divide both sides by (a+8):

 

2b/(a+8) = x

 

 

Answer 2

To solve any equation like this, you want to aim to get all the x values on one side of the equation with everything else on the other.

 

To start we need to expand the parenthesis on the right side of the equation.  We do this because we need to have the x on its own.  So:

 

8(b-x)=6b+ax -->  8b-8x=6b+ax

 

Next we want to get all the x-values on the right and the b-values on the left.  This is done so we can simplify the x-values.  To do this we need to add 8x to both sides :

 

8b-8x+8x=6b+ax+8x  -->  8b=6b+ax+8x

 

Next, we subtract 6b from both sides:

 

8b-6b=6b+ax+8x-6b  -->  2b=ax+8x

 

Now that we have all the x-values on one side of the equation, we need to simplify the terms on the right side.  By looking at the right side, we can see that x is common to both terms ax and 8x, so we can pull x out and rewrite the equation as:

 

2b=x(a+8)

 

The last step for solving this equation is getting the x term by itself.  We can do this by dividing both sides by the factor (a+8) giving us:

 

2b/(a+8)=x

 

I hope that helped