Final answer:
The slope of the function f(x) = |12x| + 3, when x > 7, is 12 units.
Step-by-step explanation:
The function f(x) = |12x| + 3 is a piecewise function where the absolute value of 12x is taken and then 3 is added. When x > 7, the function simplifies to f(x) = 12x + 3. The slope of this function is 12, which means that for every 1 unit increase in x, there is a corresponding increase of 12 units in y.