Question

What is the coefficient of the parenteses (9x - 6)? Notice that there is a negative or subtraction in front, so what are we distributing over these parentheses?

Answer 1

The expression you have is \( -(9x - 6) \). To distribute the negative sign over the parentheses, we will multiply each term inside the parentheses by \(-1\).

Here’s how the distribution works:

1. Multiply \(9x\) by \(-1\):
\[
-1 \cdot 9x = -9x
\]

2. Multiply \(-6\) by \(-1\):
\[
-1 \cdot (-6) = 6
\]

Now, combining these results, we get:
\[
-(9x - 6) = -9x + 6
\]

The coefficients of the resulting terms are:
- The coefficient of \(x\) is \(-9\).
- The constant term (which can be thought of as the coefficient of \(x^0\)) is \(6\).

To summarize, when you distribute the negative sign over the parentheses \( (9x - 6) \), the coefficient in front of \(x\) becomes \(-9\).