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5\times 4x+10x+2\times 3x=360
Multiply both sides of the equation by 10, the least common multiple of 2,5.
20x+10x+2\times 3x=360
Multiply 5 and 4 to get 20.
30x+2\times 3x=360
Combine 20x and 10x to get 30x.
30x+6x=360
Multiply 2 and 3 to get 6.
36x=360
Combine 30x and 6x to get 36x.
x=\frac{360}{36}
Divide both sides by 36.
x=10
Divide 360 by 36 to get 10.