Question

solve the equation 2 over 3 (x − 4) = 2x for x.

2

−2

−8

−4

Answer 1

\[\frac{ 2 }{ 3(x-4) } = 2x?\]

Answer 2

multiply both sides by \(\frac{3}{2}\) first

Answer 3

\[\frac{2}{3}(x-4)=2x\]
\[x-4=\frac{2}{2}\times 2x=32\]
solve
\[x-4=3x\] in two steps

Answer 4

typo, i meant
\[x-4=\frac{3}{2}\times 2x=32\]

Answer 5

ugh im so confused

Answer 6

lets go slow

Answer 7

the question is
\[\frac{2}{3}(x-4)=2x\] right?

Answer 8

yepp

Answer 9

ok so to get rid of that \(\frac{2}{3}\) out front of the parentheses, multiply both sides by the reciprocal, \(\frac{3}{2}\)

Answer 10

that just leaves \(x-4\) on the left hand side of the equal sign
the right hand side will be \(\frac{3}{2}\times 2x=3x\)

Answer 11

yeah

Answer 12

wait did you divide? I suck at this haha

Answer 13

i multiplied \(\frac{3}{2}\times 2x=\frac{3}{\cancel{2}}\cancel{2}x=3x\)

Answer 14

ooh

Answer 15

in other words, three halves of two is three

Answer 16

now you have
\[x-4=3x\] and this should be more or less easy to solve

Answer 17

idk how to solve that :/

Answer 18

\[\frac{ 2 }{ 3\left( x-4 \right)}=2x\]
2x*3(x-4)=2
\[6x ^{2}-24x=2\]
\[6x ^{2}-24x-2=0,3x ^{2}-12x-1=0\]
\[x=\frac{ 12\pm \sqrt{\left(- 12 \right)^{2}-4*3*-1} }{2*3 }\]
\[x=\frac{ 12\pm \sqrt{144+12} }{6 }=\frac{ 12\pm \sqrt{156} }{ 6 }\]
now you can solve