College Math Placement Practice Test

What is the solution for x in the equation 3 + 3x = 12 + x?

1. x = 9/2

2. x = 15/4

3. x = 5/4

4. x = 5/2

The correct answer is: x = 9/2

To solve the equation \(3 + 3x = 12 + x\), we start by isolating the variable \(x\). First, let's rearrange the equation by moving all terms involving \(x\) to one side and all constant terms to the other side. We can do this by subtracting \(x\) from both sides: \[ 3 + 3x - x = 12 + x - x \] This simplifies to: \[ 3 + 2x = 12 \] Next, subtract 3 from both sides to eliminate the constant on the left side: \[ 3 + 2x - 3 = 12 - 3 \] This results in: \[ 2x = 9 \] Now, to solve for \(x\), we need to divide both sides by 2: \[ x = \frac{9}{2} \] Thus, the solution \(x = \frac{9}{2}\) corresponds accurately to the choice provided. This correctly demonstrates that the original equation holds true when \(x\) is substituted back, confirming the validity of the solution derived.