Question

Simply the Expression:

5a + 3b - 3a + 4b + 7c

Show EVERY step, even how to do each step.

Answer 1

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:
\[
\boxed{2a + 7b + 7c}
\]