Let's first simplify the equation by distributing and combining like terms:

4(2x) - 4(1/4) - (x) - (1) = 7(x) + 7(2/7)

8x - 1 - x - 1 = 7x + 2

7x - 2 = 7x + 2

To further simplify and check the solution, let's bring the terms with x to one side:

7x - 7x = 2 + 2

0 = 4

Since 0 does not equal 4, the original equation 4(2x-1/4)-(x+1)=7(x+2/7) has no solution.