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\frac{3}{10}x+\frac{3}{10}\times 2+\frac{4}{17}\left(x+1\right)+\left(\frac{3}{10}+\frac{4}{17}\right)x=\frac{7}{12}x
Use the distributive property to multiply \frac{3}{10} by x+2.
\frac{3}{10}x+\frac{3\times 2}{10}+\frac{4}{17}\left(x+1\right)+\left(\frac{3}{10}+\frac{4}{17}\right)x=\frac{7}{12}x
Express \frac{3}{10}\times 2 as a single fraction.
\frac{3}{10}x+\frac{6}{10}+\frac{4}{17}\left(x+1\right)+\left(\frac{3}{10}+\frac{4}{17}\right)x=\frac{7}{12}x
Multiply 3 and 2 to get 6.
\frac{3}{10}x+\frac{3}{5}+\frac{4}{17}\left(x+1\right)+\left(\frac{3}{10}+\frac{4}{17}\right)x=\frac{7}{12}x
Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.
\frac{3}{10}x+\frac{3}{5}+\frac{4}{17}x+\frac{4}{17}+\left(\frac{3}{10}+\frac{4}{17}\right)x=\frac{7}{12}x
Use the distributive property to multiply \frac{4}{17} by x+1.
\frac{91}{170}x+\frac{3}{5}+\frac{4}{17}+\left(\frac{3}{10}+\frac{4}{17}\right)x=\frac{7}{12}x
Combine \frac{3}{10}x and \frac{4}{17}x to get \frac{91}{170}x.
\frac{91}{170}x+\frac{51}{85}+\frac{20}{85}+\left(\frac{3}{10}+\frac{4}{17}\right)x=\frac{7}{12}x
Least common multiple of 5 and 17 is 85. Convert \frac{3}{5} and \frac{4}{17} to fractions with denominator 85.
\frac{91}{170}x+\frac{51+20}{85}+\left(\frac{3}{10}+\frac{4}{17}\right)x=\frac{7}{12}x
Since \frac{51}{85} and \frac{20}{85} have the same denominator, add them by adding their numerators.
\frac{91}{170}x+\frac{71}{85}+\left(\frac{3}{10}+\frac{4}{17}\right)x=\frac{7}{12}x
Add 51 and 20 to get 71.
\frac{91}{170}x+\frac{71}{85}+\left(\frac{51}{170}+\frac{40}{170}\right)x=\frac{7}{12}x
Least common multiple of 10 and 17 is 170. Convert \frac{3}{10} and \frac{4}{17} to fractions with denominator 170.
\frac{91}{170}x+\frac{71}{85}+\frac{51+40}{170}x=\frac{7}{12}x
Since \frac{51}{170} and \frac{40}{170} have the same denominator, add them by adding their numerators.
\frac{91}{170}x+\frac{71}{85}+\frac{91}{170}x=\frac{7}{12}x
Add 51 and 40 to get 91.
\frac{91}{85}x+\frac{71}{85}=\frac{7}{12}x
Combine \frac{91}{170}x and \frac{91}{170}x to get \frac{91}{85}x.
\frac{91}{85}x+\frac{71}{85}-\frac{7}{12}x=0
Subtract \frac{7}{12}x from both sides.
\frac{497}{1020}x+\frac{71}{85}=0
Combine \frac{91}{85}x and -\frac{7}{12}x to get \frac{497}{1020}x.
\frac{497}{1020}x=-\frac{71}{85}
Subtract \frac{71}{85} from both sides. Anything subtracted from zero gives its negation.
x=-\frac{71}{85}\times \frac{1020}{497}
Multiply both sides by \frac{1020}{497}, the reciprocal of \frac{497}{1020}.
x=\frac{-71\times 1020}{85\times 497}
Multiply -\frac{71}{85} times \frac{1020}{497} by multiplying numerator times numerator and denominator times denominator.
x=\frac{-72420}{42245}
Do the multiplications in the fraction \frac{-71\times 1020}{85\times 497}.
x=-\frac{12}{7}
Reduce the fraction \frac{-72420}{42245} to lowest terms by extracting and canceling out 6035.