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dem82
3 months ago
13

Kate begins solving the equation StartFraction 2 Over 3 EndFraction left-parenthesis 6 x minus 3 right-parenthesis equals StartF

raction 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?
Mathematics
2 answers:
Svet_ta [12.7K]3 months ago
8 0

Answer:

The most accurate interpretation of the equation 4x=3x is that it does not have any solutions.

Step-by-step explanation:

When Kate starts to solve the equation

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

To interpret the equation effectively:

Katie follows these steps

  • \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

Upon adding 2 to each side, the equation transforms to

  • 4x-2+2=3x-2+2
  • 4x=3x

Thus 4\neq 3

Consequently, the equation does not yield any solutions.

Therefore, the interpretation stating no solution is accurate.

lawyer [12.5K]3 months ago
5 0

Answer:

The equation yields a single solution: x = 0.

Step-by-step explanation:

Took the quiz.

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