If , 2x-3/x+6=3/2 what is the value of x ?

Question

The slashes are for fractions

Answer 1

So we start with:

(2x-3)/(x+6) = (3)/(2) I'm putting all numerators and denominators in parenthesis for now

Our goal is to get "x" by itself. A pretty big obstacle is the large fraction on the left side of the equation. How will I simplify it? Multiply both sides of the equation by (x+6), because on the left side it will cancel out the denominator of that fraction, and of course what you do on one side, you have to do to the other to maintain balance. 3743

So, multiply each side by (x+6):

(x+6) * {(2x-3)/(x+6)} = 3(x+6)/(2)

On the left side, the (x+6)'s both cancel. On the right, I'm going to multiply out the 3 on the numerator.

2x - 3 = (3x + 18) / 2

We still have another fraction, and to get rid of this one, we multiply both sides of the equation by 2.

2(2x - 3) = { (3x + 18) / 2 } * 2

Multiply out the 2 on the left side of the equation, using the distributive property. And on the right side of the equation, the 2's cancel out.

4x - 6 = 3x + 18

From here, we combine our like terms. Lets subtract 3x on both sides of the equation.

x - 6 = 18

Add 6 to both sides

x = 24

Answer 2

2x-3/x+6=3/2 

4x-6/x+12=3

4x-6/x=-9

x=-2.79