Subtract : `3x+4y-2z` from the sum of `3+4z+3y-x" and "3x+2y-3z+2`.

Answer

To solve the problem of subtracting `3x + 4y - 2z` from the sum of `3 + 4z + 3y - x` and `3x + 2y - 3z + 2`, we will follow these steps:

### Step 1: Write down the expressions
We have:
1. First expression: `3 + 4z + 3y - x`
2. Second expression: `3x + 2y - 3z + 2`
3. Expression to subtract: `3x + 4y - 2z`

### Step 2: Find the sum of the first two expressions
We will add the two expressions together:
- Combine the constant terms: `3 + 2 = 5`
- Combine the `z` terms: `4z - 3z = 1z` (or just `z`)
- Combine the `y` terms: `3y + 2y = 5y`
- Combine the `x` terms: `-x + 3x = 2x`

Putting it all together, the sum is:
\[ 5 + z + 5y + 2x \]

### Step 3: Subtract the third expression from the sum
Now we need to subtract `3x + 4y - 2z` from the sum we just calculated:
\[ (5 + z + 5y + 2x) - (3x + 4y - 2z) \]

### Step 4: Distribute the negative sign
When we subtract, we need to change the signs of the terms in the expression we are subtracting:
- `3x` becomes `-3x`
- `4y` becomes `-4y`
- `-2z` becomes `+2z`

So we rewrite the expression as:
\[ 5 + z + 5y + 2x - 3x - 4y + 2z \]

### Step 5: Combine like terms
Now, we will combine the like terms:
- Constant terms: `5`
- `z` terms: `z + 2z = 3z`
- `y` terms: `5y - 4y = 1y` (or just `y`)
- `x` terms: `2x - 3x = -1x` (or just `-x`)

Putting it all together, we have:
\[ 5 + 3z + y - x \]

### Final Answer
The final result after performing the subtraction is:
\[ 5 + 3z + y - x \]

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