Question

linear equations and inequalities
katie begins solving the equation \\( \frac{2}{3}(6x - 3) = \frac{1}{2}(6x - 4) \\). her work is correct and is shown here
student’s work
\\( \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 infinite solutions.
the equation has one solution: \\( x = 0 \\).
the equation has no solution.
the equation has one solution: \\( x = \frac{4}{3} \\)

Explanation:

Step1: Analyze the equation \(4x = 3x\)

Subtract \(3x\) from both sides: \(4x - 3x = 3x - 3x\)

Step2: Simplify the equation

Simplifying gives \(x = 0\). So the equation has one solution, \(x = 0\).

Answer:

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