Which expression is equivalent to the expression below?
4q + 4r + q + q + q
Answer
A q + 4r
B 7q + 4r
C 11q
D 5q
The correct answer and explanation is:
The correct answer is B: 7q + 4r.
To explain this, let’s break down the given expression:
4q + 4r + q + q + q
- First, combine the terms with “q”:
In the expression, there are multiple “q” terms:
4q, q, q, q.
If you add these up, you get:
4q + q + q + q = 7q. - Now, consider the term with “r”:
The term “4r” is by itself and does not have any like terms to combine with, so it remains as is.
Thus, the expression simplifies to:
7q + 4r.
This is the simplest form of the given expression, as all like terms (terms with “q”) have been combined. The final result is 7q + 4r.
In summary, to simplify an algebraic expression like this, you first identify like terms (terms that have the same variable). You then combine those terms by adding or subtracting their coefficients. In this case, all the “q” terms were added together, resulting in 7q. The term 4r was left unchanged, as it had no other “r” terms to combine with. This process of combining like terms is a fundamental technique in simplifying algebraic expressions.