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12\times 7x+120=5\times 17x
Multiply both sides of the equation by 60, the least common multiple of 5,12.
84x+120=5\times 17x
Multiply 12 and 7 to get 84.
84x+120=85x
Multiply 5 and 17 to get 85.
84x+120-85x=0
Subtract 85x from both sides.
-x+120=0
Combine 84x and -85x to get -x.
-x=-120
Subtract 120 from both sides. Anything subtracted from zero gives its negation.
x=120
Multiply both sides by -1.