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\frac{1}{2}x-2+3x=5
Add 3x to both sides.
\frac{7}{2}x-2=5
Combine \frac{1}{2}x and 3x to get \frac{7}{2}x.
\frac{7}{2}x=5+2
Add 2 to both sides.
\frac{7}{2}x=7
Add 5 and 2 to get 7.
x=7\times \frac{2}{7}
Multiply both sides by \frac{2}{7}, the reciprocal of \frac{7}{2}.
x=2
Cancel out 7 and 7.