Add the following algebraic expressions :
(i) `5x^(3)- 3x + 7 , 2x^(2) - 11 and 7x^(3) - 11x^(2) + 4x- 3 `

Answer

To solve the problem of adding the algebraic expressions \(5x^3 - 3x + 7\), \(2x^2 - 11\), and \(7x^3 - 11x^2 + 4x - 3\), we will follow these steps:

### Step-by-Step Solution:

1. **Write Down the Expressions**:
We start with the three expressions:
\[ 5x^3 - 3x + 7, \quad 2x^2 - 11, \quad 7x^3 - 11x^2 + 4x - 3 \]

2. **Combine Like Terms**:
We will group the like terms together based on their degrees (powers of \(x\)):
- Cubic terms (\(x^3\)): \(5x^3\) and \(7x^3\)
- Quadratic terms (\(x^2\)): \(2x^2\) and \(-11x^2\)
- Linear terms (\(x\)): \(-3x\) and \(4x\)
- Constant terms: \(7\), \(-11\), and \(-3\)

3. **Add the Cubic Terms**:
\[ 5x^3 + 7x^3 = 12x^3 \]

4. **Add the Quadratic Terms**:
\[ 2x^2 - 11x^2 = -9x^2 \]

5. **Add the Linear Terms**:
\[ -3x + 4x = 1x \quad \text{(or simply } x\text{)} \]

6. **Add the Constant Terms**:
\[ 7 - 11 - 3 = 7 - 14 = -7 \]

7. **Combine All the Results**:
Now we can combine all the results from the previous steps:
\[ 12x^3 - 9x^2 + x - 7 \]

### Final Answer:
The sum of the given algebraic expressions is:
\[ \boxed{12x^3 - 9x^2 + x - 7} \]