Add the expressions : `3a - 2b + 5c and 4a + 7b - 9c `

Answer

To add the expressions \(3a - 2b + 5c\) and \(4a + 7b - 9c\), we will follow these steps:

### Step 1: Write down the expressions
We have two expressions:
1. \(3a - 2b + 5c\)
2. \(4a + 7b - 9c\)

### Step 2: Group like terms
We will group the like terms together. The like terms are those that have the same variable:
- The terms with \(a\): \(3a\) and \(4a\)
- The terms with \(b\): \(-2b\) and \(7b\)
- The terms with \(c\): \(5c\) and \(-9c\)

### Step 3: Add the coefficients of like terms
Now we will add the coefficients of the like terms:
- For \(a\): \(3a + 4a = (3 + 4)a = 7a\)
- For \(b\): \(-2b + 7b = (-2 + 7)b = 5b\)
- For \(c\): \(5c - 9c = (5 - 9)c = -4c\)

### Step 4: Combine the results
Now we combine the results of the like terms:
\[ 7a + 5b - 4c \]

### Final Answer
The sum of the expressions \(3a - 2b + 5c\) and \(4a + 7b - 9c\) is:
\[ 7a + 5b - 4c \]

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