Translate the word problem into an algebraic equation, as follows:
7m-3 = (1/2)(12m + 1)
Perform the indicated multiplication:
7m-3 = 6m + 1/2
Solve for m by first subtracting 6m from both sides:
m-3 = 1/2
Next, add 3 to both sides:
m = 3 1/2, or m = 7/2
The value of the variable is 7/2.