To subtract the given expressions, we need to distribute the coefficients to the terms within the parentheses and then combine like terms.
First, let's distribute the coefficients:
12(z+4) = 12z + 48
3(14z+1) = 42z + 3
Now, let's subtract the two expressions:
12z + 48 - (42z + 3)
To simplify further, we need to combine like terms:
(12z - 42z) + (48 - 3)
Combining like terms:
-30z + 45
Now, let's express the answer using fractions. To do this, we divide the result by a common factor, if possible. In this case, the common factor is 15.
Dividing both terms by 15 to express the answer in fractions:
(-30z/15) + (45/15)
Simplifying the fractions:
-2z/1 + 3/1
Finally, we can write the answer in the final form using fractions:
-2z + 3