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 is the best interpretation of this equation?

Answer 1

Answer:

The best interpretation of this equation 4x=3x is that the equation has no solution

Step-by-step explanation:

Given that Kate begins solving the equation

$\frac{2}{3}(6x-3)=\frac{1}{2}(6x-4)$

To find the best interpretation of the given equation :

Katie's steps are

• $\frac{2}{3}(6x-3)=\frac{1}{2}(6x-4)$
• $\frac{2}{3}(3(2x-1))=\frac{1}{2}((2(3x-4))$
• $2(2x-1)=1(3x-2)$
• $2(2x)+2(-1)=1(3x)+1(-2)$
• $4x-2=3x-2$

When she adds 2 to both sides, the equation becomes

• 4x-2+2=3x-2+2
• 4x=3x

Therefore $4\neq 3$

Therefore the given equation has no solution

The best interpretation of this equation 4x=3x is that the equation has no solution.

Therefore the option no solution is correct

Answer 2

Answer:

The equation has one solution: x = 0

Step-by-step explanation:

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