What is the simplified form of the expression 3x + 2 - 2x + 7?

What is the simplified form of the expression 3x + 2 - 2x + 7?

• A. x + 9
• B. 5x + 9
• C. 6x + 5
• D. 2x + 5

Answer: (A)

To simplify the expression \(3x + 2 - 2x + 7\), we need to combine like terms. Like terms are those that contain the same variable raised to the same power. In this case, the like terms are \(3x\) and \(-2x\), and the constant terms are \(2\) and \(7\). First, we combine the \(x\) terms: \[ 3x - 2x = (3 - 2)x = 1x = x \] Next, we combine the constant terms: \[ 2 + 7 = 9 \] Putting these results together gives: \[ x + 9 \] This shows that the simplified form of the expression is indeed \(x + 9\), which corresponds to the correct choice. Understanding how to combine like terms is essential in algebra, as it streamlines expressions and allows for easier manipulation and solving of equations.

To simplify the expression (3x + 2 - 2x + 7), we need to combine like terms. Like terms are those that contain the same variable raised to the same power. In this case, the like terms are (3x) and (-2x), and the constant terms are (2) and (7).

First, we combine the (x) terms:

[

3x - 2x = (3 - 2)x = 1x = x

]

Next, we combine the constant terms:

[

2 + 7 = 9

]

Putting these results together gives:

[

x + 9

]

This shows that the simplified form of the expression is indeed (x + 9), which corresponds to the correct choice. Understanding how to combine like terms is essential in algebra, as it streamlines expressions and allows for easier manipulation and solving of equations.