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48\left(2x+\frac{3}{8}\right)=8\left(6x+3\right)
Multiply both sides of the equation by 24, the least common multiple of 8,3.
96x+48\times \frac{3}{8}=8\left(6x+3\right)
Use the distributive property to multiply 48 by 2x+\frac{3}{8}.
96x+\frac{48\times 3}{8}=8\left(6x+3\right)
Express 48\times \frac{3}{8} as a single fraction.
96x+\frac{144}{8}=8\left(6x+3\right)
Multiply 48 and 3 to get 144.
96x+18=8\left(6x+3\right)
Divide 144 by 8 to get 18.
96x+18=48x+24
Use the distributive property to multiply 8 by 6x+3.
96x+18-48x=24
Subtract 48x from both sides.
48x+18=24
Combine 96x and -48x to get 48x.
48x=24-18
Subtract 18 from both sides.
48x=6
Subtract 18 from 24 to get 6.
x=\frac{6}{48}
Divide both sides by 48.
x=\frac{1}{8}
Reduce the fraction \frac{6}{48} to lowest terms by extracting and canceling out 6.