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.