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48x-24\left(2x-\frac{3x-1}{8}\right)=\frac{8}{3}\left(x+2\right)-6
Multiply both sides of the equation by 24, the least common multiple of 8,3,6,4.
48x-24\left(2x-\frac{3x-1}{8}\right)=\frac{8}{3}x+\frac{8}{3}\times 2-6
Use the distributive property to multiply \frac{8}{3} by x+2.
48x-24\left(2x-\frac{3x-1}{8}\right)=\frac{8}{3}x+\frac{8\times 2}{3}-6
Express \frac{8}{3}\times 2 as a single fraction.
48x-24\left(2x-\frac{3x-1}{8}\right)=\frac{8}{3}x+\frac{16}{3}-6
Multiply 8 and 2 to get 16.
48x-24\left(2x-\frac{3x-1}{8}\right)=\frac{8}{3}x+\frac{16}{3}-\frac{18}{3}
Convert 6 to fraction \frac{18}{3}.
48x-24\left(2x-\frac{3x-1}{8}\right)=\frac{8}{3}x+\frac{16-18}{3}
Since \frac{16}{3} and \frac{18}{3} have the same denominator, subtract them by subtracting their numerators.
48x-24\left(2x-\frac{3x-1}{8}\right)=\frac{8}{3}x-\frac{2}{3}
Subtract 18 from 16 to get -2.
48x-24\left(2x-\left(\frac{3}{8}x-\frac{1}{8}\right)\right)=\frac{8}{3}x-\frac{2}{3}
Divide each term of 3x-1 by 8 to get \frac{3}{8}x-\frac{1}{8}.
48x-24\left(2x-\frac{3}{8}x-\left(-\frac{1}{8}\right)\right)=\frac{8}{3}x-\frac{2}{3}
To find the opposite of \frac{3}{8}x-\frac{1}{8}, find the opposite of each term.
48x-24\left(2x-\frac{3}{8}x+\frac{1}{8}\right)=\frac{8}{3}x-\frac{2}{3}
The opposite of -\frac{1}{8} is \frac{1}{8}.
48x-24\left(\frac{13}{8}x+\frac{1}{8}\right)=\frac{8}{3}x-\frac{2}{3}
Combine 2x and -\frac{3}{8}x to get \frac{13}{8}x.
48x-24\times \frac{13}{8}x-24\times \frac{1}{8}=\frac{8}{3}x-\frac{2}{3}
Use the distributive property to multiply -24 by \frac{13}{8}x+\frac{1}{8}.
48x+\frac{-24\times 13}{8}x-24\times \frac{1}{8}=\frac{8}{3}x-\frac{2}{3}
Express -24\times \frac{13}{8} as a single fraction.
48x+\frac{-312}{8}x-24\times \frac{1}{8}=\frac{8}{3}x-\frac{2}{3}
Multiply -24 and 13 to get -312.
48x-39x-24\times \frac{1}{8}=\frac{8}{3}x-\frac{2}{3}
Divide -312 by 8 to get -39.
48x-39x+\frac{-24}{8}=\frac{8}{3}x-\frac{2}{3}
Multiply -24 and \frac{1}{8} to get \frac{-24}{8}.
48x-39x-3=\frac{8}{3}x-\frac{2}{3}
Divide -24 by 8 to get -3.
9x-3=\frac{8}{3}x-\frac{2}{3}
Combine 48x and -39x to get 9x.
9x-3-\frac{8}{3}x=-\frac{2}{3}
Subtract \frac{8}{3}x from both sides.
\frac{19}{3}x-3=-\frac{2}{3}
Combine 9x and -\frac{8}{3}x to get \frac{19}{3}x.
\frac{19}{3}x=-\frac{2}{3}+3
Add 3 to both sides.
\frac{19}{3}x=-\frac{2}{3}+\frac{9}{3}
Convert 3 to fraction \frac{9}{3}.
\frac{19}{3}x=\frac{-2+9}{3}
Since -\frac{2}{3} and \frac{9}{3} have the same denominator, add them by adding their numerators.
\frac{19}{3}x=\frac{7}{3}
Add -2 and 9 to get 7.
x=\frac{7}{3}\times \frac{3}{19}
Multiply both sides by \frac{3}{19}, the reciprocal of \frac{19}{3}.
x=\frac{7\times 3}{3\times 19}
Multiply \frac{7}{3} times \frac{3}{19} by multiplying numerator times numerator and denominator times denominator.
x=\frac{7}{19}
Cancel out 3 in both numerator and denominator.