To simplify the expression \(5a + 3b - 3a + 4b + 7c\), we will follow these steps:
Step 1: Group like terms
We identify the similar terms in the expression. The terms can be grouped as follows:
- Terms with \(a\): \(5a\) and \(-3a\)
- Terms with \(b\): \(3b\) and \(4b\)
- Constant term with \(c\): \(7c\)
Step 2: Simplify each group
Now we will simplify each group of like terms:
Combining terms with \(a\):
\[ 5a - 3a \] To perform this operation, subtract the coefficients: \[ 5 - 3 = 2 \] So, \[ 5a - 3a = 2a \]
Combining terms with \(b\):
\[ 3b + 4b \] Again, we add the coefficients: \[ 3 + 4 = 7 \] So, \[ 3b + 4b = 7b \]
Constant term with \(c\):
The term \(7c\) does not combine with any other terms since there are no other \(c\) terms present.
Step 3: Write the simplified expression
Now we can combine all the simplified groups together: \[ 2a + 7b + 7c \]
Final Result
Thus, the simplified expression is: \[ \boxed{2a + 7b + 7c} \]