Which algebraic expression is equivalent to the expression below?

Question

23x + 9 - 5x
A.
18(x + 1)
B.
9(x + 1)
C.
9(2x + 1)
D.
9(2x - 1)

Answer 1

To simplify the expression \(23x + 9 - 5x\), we start by combining like terms.

1. Combine the \(x\) terms: \[ 23x - 5x = 18x \]

2. Now, add the constant term: \[ 18x + 9 \]

Now we have the simplified expression: \[ 18x + 9 \]

Next, we can factor this expression. Notice that both terms share a common factor of 9: \[ 18x + 9 = 9(2x + 1) \]

Thus, the equivalent algebraic expression is: \[ 9(2x + 1) \]

The correct answer is: C. 9(2x + 1)