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x-\frac{1}{12}=\frac{5}{8}
Swap sides so that all variable terms are on the left hand side.
x=\frac{5}{8}+\frac{1}{12}
Add \frac{1}{12} to both sides.
x=\frac{15}{24}+\frac{2}{24}
Least common multiple of 8 and 12 is 24. Convert \frac{5}{8} and \frac{1}{12} to fractions with denominator 24.
x=\frac{15+2}{24}
Since \frac{15}{24} and \frac{2}{24} have the same denominator, add them by adding their numerators.
x=\frac{17}{24}
Add 15 and 2 to get 17.