The sum of `4x - 3y - 7z, x -y -z and - 2x- 3y+ 4z` is

Options

A. `3x - 7y - 4z`
B. `3x - y + 4z`
C. `3x + y - 4z`
D. `3x + y + 4z`

Answer

To find the sum of the expressions \(4x - 3y - 7z\), \(x - y - z\), and \(-2x - 3y + 4z\), we will follow these steps:

### Step 1: Write down the expressions
We have the following expressions:
1. \(4x - 3y - 7z\)
2. \(x - y - z\)
3. \(-2x - 3y + 4z\)

### Step 2: Combine like terms
We will combine the coefficients of \(x\), \(y\), and \(z\) from all three expressions.

**For \(x\):**
- From \(4x\), we have \(4\).
- From \(x\), we have \(1\).
- From \(-2x\), we have \(-2\).

So, the total coefficient of \(x\) is:
\[ 4 + 1 - 2 = 3 \]

**For \(y\):**
- From \(-3y\), we have \(-3\).
- From \(-y\), we have \(-1\).
- From \(-3y\), we have \(-3\).

So, the total coefficient of \(y\) is:
\[ -3 - 1 - 3 = -7 \]

**For \(z\):**
- From \(-7z\), we have \(-7\).
- From \(-z\), we have \(-1\).
- From \(4z\), we have \(4\).

So, the total coefficient of \(z\) is:
\[ -7 - 1 + 4 = -4 \]

### Step 3: Write the final expression
Now, we can combine all the coefficients we calculated:
\[ 3x - 7y - 4z \]

### Final Answer
The sum of the expressions \(4x - 3y - 7z\), \(x - y - z\), and \(-2x - 3y + 4z\) is:
\[ 3x - 7y - 4z \]

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