Question

A is a constant. Find A such that the equation 2x + 1 = 2A + 3(x + A) has a solution at x = 2.

Answer 1

                 2x + 1  =  2A + 3(x + A)

You want x=2 to be a solution.
So the equation will be a true statement when

                 2(2) + 1  =  2A + 3(2 + A)

                     4 + 1  =  2A + 6 + 3A

Combine like terms:  5 = 5A + 6

Subtract 6 from each side:  -1 = 5A

Divide each side by  5:      -0.2  =  A