horsegirl27
  • horsegirl27
help please
Mathematics
katieb
  • katieb
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horsegirl27
  • horsegirl27
Solve for x: 2/3(x-2)=4x I get confused when there are fractions :/ please help :)
horsegirl27
  • horsegirl27
Answer choices: -2/5 -5/2 2/5 5
horsegirl27
  • horsegirl27

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pooja195
  • pooja195
Anytime you see paretheses we need to see if we can distribute \[\huge~\rm~2/3(x-2)=4x\] can we?
anonymous
  • anonymous
divide it, the answer is 5?
horsegirl27
  • horsegirl27
yes
horsegirl27
  • horsegirl27
So 2/3x -1 1/3=4x?
pooja195
  • pooja195
something is not right \[\huge~\rm~( 2 /3 )(x)+( 2/ 3 )(−2)=4x(Distribute)\]
anonymous
  • anonymous
sorry my mistake the answer is - 2/5
pooja195
  • pooja195
@chris88 it would help if you explained your answer. @horsegirl27 what is 2/3*-2?
horsegirl27
  • horsegirl27
ohhh i see my mistake, -1 1/3?
pooja195
  • pooja195
turn that into an IMPROPER fraction
pooja195
  • pooja195
\[\huge~\rm~2 /3 x+ −4 /3 =4x\]
pooja195
  • pooja195
whats the next step?
pooja195
  • pooja195
Subtract 4x from both sides. \[\huge~\rm~2 /3 x-4x+ −4 /3 =4x-4x\] \[\huge~\rm~-10/3-4/3=0\] Add 4/3 to both sides. \[\huge~\rm~-10/3+4/3 −4 /3 =0+4/3\] \[\huge~\rm~−10/ 3 x= 4/ 3\] multiply by the reciprocal (flip fraction to 3/-10) \[\rm~( 3 −10 )*( −10 /3 x)=( 3/ −10 )*( 4 /3 )\]
pooja195
  • pooja195
once you do that you get your answer
anonymous
  • anonymous
i dunno whether is correct or not, below is my solution: 2/3 = 4x / (x-2) 2(x-2) = 12x 2x - 4 = 12 x -4 = 12x-2x -4 = 10x x= 4/-10 x = -2/5
TheSmartOne
  • TheSmartOne
\(\sf\Large\frac{2}{3}(x-2)=4x\) Multiply by the reciprocal of \(\sf\Large \frac{2}{3}\) on both sides. The reciprocal of \(\sf\Large \frac{a}{b}\) is \(\sf\Large \frac{b}{a}\)
TheSmartOne
  • TheSmartOne
After you tell me what you get, we can move on to the next step :P
horsegirl27
  • horsegirl27
Sorry, my computer froze! xD
anonymous
  • anonymous
yes, the smart one solution of reciprocal method is right :)

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