The Correct Answer and Explanation is:
The correct answer is 9a + 7.
To solve this problem, you need to simplify the algebraic expression by combining like terms. Like terms are parts of the expression that contain the same variable raised to the same power. In this case, the terms with the variable ‘a’ are like terms, and the constant number is a separate term.
The original expression is:
12a – 4a + 7 + a
First, identify all the terms that contain the variable ‘a’. These are 12a, -4a, and +a. It is important to remember that a variable standing alone, like ‘a’, has an implied coefficient of 1. So, we can think of it as +1a.
Let’s group these like terms together to make the calculation clearer:
(12a – 4a + 1a) + 7
Now, combine the coefficients (the numbers in front of the variable ‘a’) of these terms:
12 – 4 + 1
Working from left to right, we first calculate 12 minus 4, which equals 8. Then, we add 1 to that result: 8 + 1 equals 9. This means the combined ‘a’ term is 9a.
Next, we look at the constant terms, which are the numbers without any variables attached. In this expression, the only constant term is +7. Since there are no other constant numbers to add to or subtract from it, this term remains as it is.
Finally, we put the simplified variable term and the constant term together to get the final answer. Combining the 9a we calculated and the constant 7 gives us the fully simplified expression: 9a + 7. This matches the blue option provided in the image.
