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baherus [9]
3 years 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:
mixas84 [53]3 years ago
8 0

Answer:

<h3>The best interpretation of this equation 4x=3x is that the equation has no solution</h3>

Step-by-step explanation:

Given that Kate begins solving the equation

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

<h3>To find the best interpretation of the given equation :</h3><h3>Katie's steps are</h3>
  • \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

<h3>Therefore the given equation has no solution </h3><h3>The best interpretation of this equation 4x=3x is that the equation has no solution.</h3><h3>Therefore the option no solution is correct</h3>
Zinaida [17]3 years ago
5 0

Answer:

The equation has one solution: x = 0

Step-by-step explanation:

took the quiz

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