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4\times 2x+3\times 3x=60
Multiply both sides of the equation by 12, the least common multiple of 3,4.
8x+3\times 3x=60
Multiply 4 and 2 to get 8.
8x+9x=60
Multiply 3 and 3 to get 9.
17x=60
Combine 8x and 9x to get 17x.
x=\frac{60}{17}
Divide both sides by 17.