Question

kate begins solving the equation \\(\frac{2}{3}(6x - 3) = \frac{1}{2}(6x - 4)\\). her work is correct and is shown below.\\(\frac{2}{3}(6x - 3) = \frac{1}{2}(6x - 4)\\)\\(4x - 2 = 3x - 2\\)when she adds 2 to both sides, the equation \\(4x = 3x\\) results. which solution will best illustrate what happens to x ?\\(\circ\\) the equation has infinite solutions.\\(\circ\\) the equation has one solution: \\(x = 0\\).\\(\circ\\) the equation has one solution: \\(x = \frac{4}{3}\\).\\(\circ\\) the equation has no solution.

Explanation:

Step1: Simplify the final equation

Start with the equation after adding 2 to both sides:
$$4x = 3x$$

Step2: Isolate the variable x

Subtract $3x$ from both sides to get x alone:
$$4x - 3x = 3x - 3x$$
$$x = 0$$

Answer:

The equation has one solution: $x = 0$