If `P=3x-4y-8z, Q=-10y+7x+11z and R=19z-6y+4x`, then `P-Q+R` is equal to

Options

A. `13x-20y+16z`
B. 0
C. `x+y+z`
D. `2x-4y+3z`

Answer

To solve the expression \( P - Q + R \) where:

- \( P = 3x - 4y - 8z \)
- \( Q = -10y + 7x + 11z \)
- \( R = 19z - 6y + 4x \)

we will follow these steps:

### Step 1: Write down the expression
We start with the expression:
\[ P - Q + R = (3x - 4y - 8z) - (-10y + 7x + 11z) + (19z - 6y + 4x) \]

### Step 2: Distribute the negative sign
Distributing the negative sign across \( Q \):
\[ P - Q + R = 3x - 4y - 8z + 10y - 7x - 11z + 19z - 6y + 4x \]

### Step 3: Combine like terms
Now, we will combine the like terms for \( x \), \( y \), and \( z \).

**For \( x \):**
\[ 3x - 7x + 4x = (3 - 7 + 4)x = 0x \]

**For \( y \):**
\[ -4y + 10y - 6y = (-4 + 10 - 6)y = 0y \]

**For \( z \):**
\[ -8z - 11z + 19z = (-8 - 11 + 19)z = 0z \]

### Step 4: Write the final result
Putting it all together:
\[ P - Q + R = 0x + 0y + 0z = 0 \]

Thus, the final answer is:
\[ \boxed{0} \]