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10=\frac{2\times 12}{3}x+2
Express \frac{2}{3}\times 12 as a single fraction.
10=\frac{24}{3}x+2
Multiply 2 and 12 to get 24.
10=8x+2
Divide 24 by 3 to get 8.
8x+2=10
Swap sides so that all variable terms are on the left hand side.
8x=10-2
Subtract 2 from both sides.
8x=8
Subtract 2 from 10 to get 8.
x=\frac{8}{8}
Divide both sides by 8.
x=1
Divide 8 by 8 to get 1.