Which of the following is the correct simplification of the expression 3a + 5b - 2a + 4b?

• A. a + 9b
• B. 5a + 9b
• C. 3a + 9b
• D. 3a + 2b

Answer: (A)

To simplify the expression 3a + 5b - 2a + 4b, it is essential to combine like terms. Like terms are those that contain the same variable raised to the same power.

First, look at the terms containing the variable 'a':

• You have 3a and -2a.

To combine these, we perform the operation:

3a - 2a = (3 - 2)a = 1a or simply a.

Next, focus on the terms that have the variable 'b':

• You have 5b and 4b.

To combine these, add them together:

5b + 4b = (5 + 4)b = 9b.

Putting it all together, after combining the like terms, we end up with:

a + 9b.

This final expression, a + 9b, corresponds perfectly with the selected answer, showing that it is indeed the correct simplification of the original expression.