Add the following algebraic expressions :
`2a - 3b + 4c , -3a + 2b - 5c , 7a - c and 3b + 6c `

Answer

To add the algebraic expressions \(2a - 3b + 4c\), \(-3a + 2b - 5c\), \(7a - c\), and \(3b + 6c\), we will follow these steps:

### Step 1: Write down all the expressions
We start by writing down all the given expressions:
\[ 2a - 3b + 4c, \quad -3a + 2b - 5c, \quad 7a - c, \quad 3b + 6c \]

### Step 2: Combine like terms
We will combine the terms with the same variables (like terms). We will group the coefficients of \(a\), \(b\), and \(c\) together.

- **For \(a\)**:
- From \(2a\), \(-3a\), and \(7a\):
\[ 2a - 3a + 7a \]

- **For \(b\)**:
- From \(-3b\), \(2b\), \(3b\):
\[ -3b + 2b + 3b \]

- **For \(c\)**:
- From \(4c\), \(-5c\), \(-c\), and \(6c\):
\[ 4c - 5c - c + 6c \]

### Step 3: Calculate the coefficients
Now, we will calculate the coefficients for each variable.

- **Calculating \(a\)**:
\[ 2 - 3 + 7 = 6 \]
So, the coefficient of \(a\) is \(6\).

- **Calculating \(b\)**:
\[ -3 + 2 + 3 = 2 \]
So, the coefficient of \(b\) is \(2\).

- **Calculating \(c\)**:
\[ 4 - 5 - 1 + 6 = 4 \]
So, the coefficient of \(c\) is \(4\).

### Step 4: Write the final expression
Now we can write the final expression by combining the coefficients we calculated:
\[ 6a + 2b + 4c \]

### Final Answer
Thus, the sum of the given algebraic expressions is:
\[ \boxed{6a + 2b + 4c} \]

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