Subtract `12x + 3y - z` from the sum of `7x + 4y - 5z + 5` and `6x - 7z - 8`.

Answer

To solve the problem, we will follow these steps:

### Step 1: Find the sum of the two expressions
We need to sum the expressions \(7x + 4y - 5z + 5\) and \(6x - 7z - 8\).

\[ (7x + 4y - 5z + 5) + (6x - 7z - 8) \]

### Step 2: Combine like terms
Now, we combine the like terms from the sum:

- Combine the \(x\) terms: \(7x + 6x = 13x\)
- Combine the \(y\) terms: \(4y\) (there's no other \(y\) term)
- Combine the \(z\) terms: \(-5z - 7z = -12z\)
- Combine the constant terms: \(5 - 8 = -3\)

So, the sum is:

\[ 13x + 4y - 12z - 3 \]

### Step 3: Subtract the second expression from the sum
Now, we need to subtract \(12x + 3y - z\) from the result we obtained:

\[ (13x + 4y - 12z - 3) - (12x + 3y - z) \]

### Step 4: Distribute the negative sign
Distributing the negative sign gives us:

\[ 13x + 4y - 12z - 3 - 12x - 3y + z \]

### Step 5: Combine like terms again
Now, we combine the like terms:

- Combine the \(x\) terms: \(13x - 12x = 1x\) or simply \(x\)
- Combine the \(y\) terms: \(4y - 3y = 1y\) or simply \(y\)
- Combine the \(z\) terms: \(-12z + z = -11z\)
- The constant term remains: \(-3\)

So, the final expression after subtraction is:

\[ x + y - 11z - 3 \]

### Final Answer
The final result is:

\[ x + y - 11z - 3 \]

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