Which statement is true about the following equation?
6(7-2x)=-12x+42
It has no solution.
It has infinitely many solutions.
It has exactly one solution, x = 6.
It has exactly one solution, x = 0.
It has exactly one solution, x = 6.
To determine if the given equation has a solution, we can solve it step-by-step:
Step 1: Distribute the 6 on the left side of the equation:
42 - 12x = -12x + 42
Step 2: Simplify the equation by combining like terms:
-12x + 12x = 42 - 42
0 = 0
Step 3: Analyze the simplified equation.
Since the equation simplifies to 0 = 0, this means that both sides of the equation are equal to each other for any value of x. In other words, any value of x will satisfy the equation. Hence, the given equation has infinitely many solutions.
Therefore, the correct answer is: It has infinitely many solutions.