Question

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

• the equation has one solution: \\(x = 0\\).\
• the equation has no solution.\
• the equation has infinite solutions.\
• the equation has one solution: \\(x = \frac{4}{3}\\).

Explanation:

Step1: Start with the equation after adding 2

We have the equation \( 4x = 3x \).

Step2: Subtract \( 3x \) from both sides

Subtract \( 3x \) from each side: \( 4x - 3x=3x - 3x \).
Simplify both sides: \( x = 0 \).
So the equation has one solution, \( x = 0 \).

Answer:

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