What should be added to `7a-9b+13c` to get `9a+b-c`?

Answer

To find out what should be added to the expression \(7a - 9b + 13c\) to get \(9a + b - c\), we can follow these steps:

### Step 1: Set up the equation
We need to find an expression \(x\) such that:
\[ 7a - 9b + 13c + x = 9a + b - c \]

### Step 2: Isolate \(x\)
To find \(x\), we can rearrange the equation:
\[ x = (9a + b - c) - (7a - 9b + 13c) \]

### Step 3: Simplify the right-hand side
Now, we will simplify the expression on the right-hand side:
\[ x = 9a + b - c - 7a + 9b - 13c \]

### Step 4: Combine like terms
Now, we will combine the like terms:
- For \(a\): \(9a - 7a = 2a\)
- For \(b\): \(b + 9b = 10b\)
- For \(c\): \(-c - 13c = -14c\)

Putting it all together, we get:
\[ x = 2a + 10b - 14c \]

### Conclusion
Thus, the expression that should be added to \(7a - 9b + 13c\) to get \(9a + b - c\) is:
\[ \boxed{2a + 10b - 14c} \]

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