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

Answer:

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

Step-by-step explanation:

The equation Kate is solving is: $\dfrac{2}{3} (6x-3)=\dfrac{1}{2}(6x-4)$

$\dfrac{2(6x-3)}{3}=\dfrac{(6x-4)}{2}\\\dfrac{2*3(2x-1)}{3}=\dfrac{2(3x-2)}{2}\\4x-2=3x-2\\ Adding two both sides \\4x=3x\\4x-3x=0\\x=0$

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