kate begins solving the equation $\frac{2}{3}(6x - 3)=\frac{1}{2}(6x - 4)$. her work is correct and is shown…

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

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

Answer

Explanation:

Step1: Start with the equation after adding 2

We have the equation (4x - 2=3x - 2). After adding 2 to both sides, we get (4x-2 + 2=3x-2 + 2).

Step2: Simplify both sides

Simplifying gives (4x=3x). Then subtract (3x) from both sides: (4x-3x=3x - 3x).

Step3: Solve for x

We obtain (x = 0).

Answer:

The equation has one solution: (x = 0).