Use the transposition method to solve given linear equation in one variable:x/2 - 1/2 = x/3 + 1/4

Sure, let's solve the equation step by step:

1. First, let's get rid of the fractions by multiplying the entire equation by the least common multiple (LCM) of 2, 3, and 4, which is 12. This gives us:

   12*(x/2 - 1/2) = 12*(x/3 + 1/4)

   Simplifying this, we get:

   6x - 6 = 4x + 3

2. Next, let's isolate x by subtracting 4x from both sides of the equation:

   6x - 4x - 6 = 4x - 4x + 3

   Simplifying this, we get:

   2x - 6 = 3

3. Finally, let's solve for x by adding 6 to both sides of the equation:

   2x - 6 + 6 = 3 + 6

   Simplifying this, we get:

   2x = 9

   Dividing both sides by 2, we get:

   x = 9/2 = 4.5

So, the solution to the equation x/2 - 1/2 = x/3 + 1/4 is x = 4.5.