The multiplicative inverse of a number is what you can multiply that number by to get 1. In this case, we need to find the multiplicative inverse of the expression 4c + 5, where c is a real number.
To find the multiplicative inverse, we need to consider the expression itself. The multiplicative inverse of a number x is given by 1/x. So, for our expression 4c + 5, the multiplicative inverse would be:
Multiplicative Inverse = 1 / (4c + 5)
It is important to note that the inverse is defined as long as 4c + 5 is not equal to zero. Thus, we must ensure that the value of c does not make the expression equal to zero, specifically:
4c + 5 ≠ 0
Solving for c, we find:
4c ≠ -5 → c ≠ -5/4
In conclusion, the multiplicative inverse of 4c + 5 is 1 / (4c + 5), valid for all real numbers c except c = -5/4.