To solve the given equation 2(3x-1) 7/2=5x-2(2x-7), we will follow the steps below:

Step 1: Simplify the equation by distributing and combining like terms

2(3x-1) + 7/2 = 5x - 2(2x-7)

Multiply 2 with each term inside the parentheses:
6x - 2 + 7/2 = 5x - 4x + 14

Combine like terms:
6x - 2 + 7/2 = x + 14

Step 2: Convert the mixed number (7/2) to an improper fraction

To add fractions, we need to have a common denominator. In this case, the common denominator is 2.

7/2 can be converted to an improper fraction by multiplying the whole number (7) by the denominator (2) and adding the numerator (7) to the result. This gives us:
7/2 = (7 * 2 + 7)/2 = 21/2

So, the equation becomes:
6x - 2 + 21/2 = x + 14

Step 3: Combine the constants on one side and the variables on the other side

To isolate the variable (x), we need to move the constants to one side of the equation and the variables to the other side. We can do this by subtracting x from both sides and adding 2 to both sides:

6x - x = 14 - 2 - 21/2

Combine like terms:
5x = 12 - 21/2

Step 4: Simplify the right side of the equation

To subtract fractions, we need to have a common denominator. In this case, the common denominator is 2.

12 can be converted to a fraction with a denominator of 2 by multiplying it by 2/2:
12 = (12 * 2)/2 = 24/2

So, the equation becomes:
5x = 24/2 - 21/2

Subtract the fractions:
5x = (24 - 21)/2 = 3/2

Step 5: Solve for x

To solve for x, divide both sides of the equation by 5:

(5x)/5 = (3/2)/5

Simplify:
x = 3/10

Therefore, the solution to the equation 2(3x-1) 7/2=5x-2(2x-7) is x = 3/10.