How many solutions can be found for the linear equation?

Question

3(x + 4) = 3x + 4
Responses
A no solutionno solution
B one solutionone solution
C two solutionstwo solutions
D infinitely many solutions

Answer 1

To determine how many solutions exist for the linear equation \( 3(x + 4) = 3x + 4 \), we can simplify the equation step by step:

1. Distribute on the left side: \[ 3(x + 4) = 3x + 12 \] So, the equation becomes: \[ 3x + 12 = 3x + 4 \]

2. Next, we can subtract \( 3x \) from both sides: \[ 12 = 4 \]

This statement \( 12 = 4 \) is false, which indicates that the original equation does not hold true for any value of \( x \).

Since the equation leads us to a contradiction, we conclude that there are no possible solutions.

Therefore, the correct answer is: A. no solution.