Add:
`6ax - 2by + 3cz, 6by - 11ax - cz and 1- cz - 2ax - 3by`

Answer

To solve the problem of adding the algebraic expressions \(6ax - 2by + 3cz\), \(6by - 11ax - cz\), and \(1 - cz - 2ax - 3by\), we will follow these steps:

### Step 1: Write down the expressions
We start by writing down the three algebraic expressions clearly:
1. \(6ax - 2by + 3cz\)
2. \(6by - 11ax - cz\)
3. \(1 - cz - 2ax - 3by\)

### Step 2: Group like terms
Next, we will group the like terms together. The like terms are those that contain the same variables:
- Terms with \(ax\): \(6ax\), \(-11ax\), and \(-2ax\)
- Terms with \(by\): \(-2by\), \(6by\), and \(-3by\)
- Terms with \(cz\): \(3cz\), \(-cz\), and \(-cz\)
- Constant term: \(1\)

### Step 3: Combine the coefficients of like terms
Now we will combine the coefficients of the like terms:

- For \(ax\):
\[ 6ax - 11ax - 2ax = (6 - 11 - 2)ax = -7ax \]

- For \(by\):
\[ -2by + 6by - 3by = (-2 + 6 - 3)by = 1by = by \]

- For \(cz\):
\[ 3cz - cz - cz = (3 - 1 - 1)cz = 1cz = cz \]

- The constant term is simply \(1\).

### Step 4: Write the final expression
Putting all the combined terms together, we get:
\[ -7ax + by + cz + 1 \]

### Final Answer
Thus, the final answer after adding the three algebraic expressions is:
\[ -7ax + by + cz + 1 \]

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