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5\times 3x-60=2\times 7x
Multiply both sides of the equation by 20, the least common multiple of 4,10.
15x-60=2\times 7x
Multiply 5 and 3 to get 15.
15x-60=14x
Multiply 2 and 7 to get 14.
15x-60-14x=0
Subtract 14x from both sides.
x-60=0
Combine 15x and -14x to get x.
x=60
Add 60 to both sides. Anything plus zero gives itself.