To determine the multiplicative inverse of \(4c + 5\), follow these steps:
1. Understand what a multiplicative inverse is:
The multiplicative inverse of a number \(a\) is another number \(b\) such that when \(a\) is multiplied by \(b\), the result is \(1\). Mathematically, \(a \cdot b = 1\).
2. Identify the expression whose inverse is needed:
Here, we need the multiplicative inverse of \(4c + 5\).
3. Set up the equation for the multiplicative inverse:
To find the multiplicative inverse of \(4c + 5\), we look for a term that will satisfy the equation \((4c + 5) \cdot \text{Inverse} = 1\).
4. Solve for the inverse:
Let the multiplicative inverse be \( \frac{1}{4c + 5} \). To verify, check that:
[tex]\[
(4c + 5) \cdot \frac{1}{4c + 5} = 1
\][/tex]
This confirms that \(\frac{1}{4c + 5}\) is indeed the multiplicative inverse of \(4c + 5\).
Therefore, the multiplicative inverse of \(4c + 5\) is \(\frac{1}{4c + 5}\).
Among the given options, the correct one is [tex]\(\frac{1}{4c + 5}\)[/tex].
