Coefficient of x in `(x + 6) (7-3x)` is ____

Options

A. 42
B. `-3`
C. 7
D. `-11`

Answer

To find the coefficient of \( x \) in the expression \( (x + 6)(7 - 3x) \), we will follow these steps:

### Step 1: Expand the expression
We start by distributing each term in the first bracket \( (x + 6) \) with each term in the second bracket \( (7 - 3x) \).

\[ (x + 6)(7 - 3x) = x \cdot 7 + x \cdot (-3x) + 6 \cdot 7 + 6 \cdot (-3x) \]

### Step 2: Perform the multiplications
Now, we calculate each multiplication:

1. \( x \cdot 7 = 7x \)
2. \( x \cdot (-3x) = -3x^2 \)
3. \( 6 \cdot 7 = 42 \)
4. \( 6 \cdot (-3x) = -18x \)

Putting these together, we have:

\[ 7x - 3x^2 + 42 - 18x \]

### Step 3: Combine like terms
Now we combine the like terms in the expression:

\[ -3x^2 + (7x - 18x) + 42 = -3x^2 - 11x + 42 \]

### Step 4: Identify the coefficient of \( x \)
The coefficient of \( x \) in the expression \( -3x^2 - 11x + 42 \) is the number that multiplies \( x \), which is \( -11 \).

Thus, the coefficient of \( x \) is:

\[ \text{Coefficient of } x = -11 \]

### Final Answer
The coefficient of \( x \) in the expression \( (x + 6)(7 - 3x) \) is \( -11 \).

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