Question

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.

Answer 1

B The equation has one solution: x = 0.

Explanation:

Answer 2

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

Explanation:

The equation Kate is solving is:
`(2)/(3) (6x-3)=(1)/(2)(6x-4)`

`(2(6x-3))/(3)=((6x-4))/(2)\\(2*3(2x-1))/(3)=(2(3x-2))/(2)\\4x-2=3x-2\\$Adding two both sides$\\4x=3x\\4x-3x=0\\x=0`

Therefore, the equation has one solution: x = 0.