To simplify the expression \( 5a + 6b + 7a \), you can follow these steps:

### Step 1: Identify Like Terms
- Like terms are terms that have the same variable raised to the same power.
- In this expression, \( 5a \) and \( 7a \) are like terms because they both contain the variable \( a \).
- \( 6b \) is not a like term with \( 5a \) and \( 7a \) because it has a different variable, \( b \).

### Step 2: Combine Like Terms
- Add the coefficients (the numerical parts) of the like terms.
- \( 5a + 7a = (5 + 7)a = 12a \).

### Step 3: Write the Final Expression
- Combine the simplified like terms with the remaining term.
- The expression simplifies to \( 12a + 6b \).

### Final Answer
The simplified expression is \( \mathbf{12a + 6b} \).

Would you like more details or have any questions? Here are some related questions:

1. How do you identify like terms in more complex expressions?
2. What is the procedure for simplifying expressions with multiple variables and powers?
3. How do you factor out common factors from an expression?
4. How does the distributive property apply to expressions like this?
5. Can you simplify an expression with fractions or decimals in the same way?

**Tip:** When simplifying expressions, always group and combine like terms first to make the process easier.

Learn how to simplify the expression 5a + 6b + 7a step-by-step with our detailed guide. This problem covers algebraic concepts such as combining like terms and simplifying expressions. Suitable for students in Grades 7-9.

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