Last final question thats giving me troubles even though it seems really easy. asap please :)

Question

Solve

 

 x-2   = 1 +  x-3

2x+1    2       2x  

 

• Thanks a ton!

Answer 1

Are you meaning to write fractions? If so you should write them in a better format such as:
(x-2)/(2x+1) = (1/2) + (x-3)/(2x).

If that is the real question, then use a common denominator on the right side of the equation to get (x/2x) + (x-3)/(2x) so the right side becomes (2x-3)/(2x).

Now your equation is a proportion.

(x-2)/(2x+1) =(2x-3)/(2x). By cross-multiplying you can get

4x² - 4x -3 = 2x²-4x. Subtract 2x²-4x from both sides leaving

2x²-3 = 0.

Then 2x² = 3 and x² = 3/2.

Take the square root of both sides to get x = ±√(3/2) or ±(√6)/2