Asked by martin

Kate begins solving the equation StartFraction 2 Over 3 EndFraction left-parenthesis 6 x minus 3 right-parenthesis equals StartFraction one-half EndFraction left-parenthesis 6 x minus 4 left-parenthesis.(6x – 3) = StartFraction 2 Over 3 EndFraction left-parenthesis 6 x minus 3 right-parenthesis equals StartFraction one-half EndFraction left-parenthesis 6 x minus 4 left-parenthesis.(6x – 4). Her work is correct and is shown below.

StartFraction 2 Over 3 EndFraction left-parenthesis 6 x minus 3 right-parenthesis equals StartFraction one-half EndFraction left-parenthesis 6 x minus 4 left-parenthesis.(6x – 3) = StartFraction 2 Over 3 EndFraction left-parenthesis 6 x minus 3 right-parenthesis equals StartFraction one-half EndFraction left-parenthesis 6 x minus 4 left-parenthesis.(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 one solution: x = StartFraction 4 Over 3 EndFraction..
The equation has no solution.

All Answers 1

Answered by GPT-5 mini AI
Solve: (2/3)(6x − 3) = (1/2)(6x − 4)

Left side = 4x − 2, right side = 3x − 2, so 4x − 2 = 3x − 2.
Add 2: 4x = 3x. Subtract 3x: x = 0.

Thus: The equation has one solution: x = 0.