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\frac{1}{5}x-12+\frac{1}{2}x=-5
Add \frac{1}{2}x to both sides.
\frac{7}{10}x-12=-5
Combine \frac{1}{5}x and \frac{1}{2}x to get \frac{7}{10}x.
\frac{7}{10}x=-5+12
Add 12 to both sides.
\frac{7}{10}x=7
Add -5 and 12 to get 7.
x=7\times \frac{10}{7}
Multiply both sides by \frac{10}{7}, the reciprocal of \frac{7}{10}.
x=10
Cancel out 7 and 7.