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117\times 18x+26\times 7x=18\times 28x
Multiply both sides of the equation by 468, the least common multiple of 4,18,26.
2106x+26\times 7x=18\times 28x
Multiply 117 and 18 to get 2106.
2106x+182x=18\times 28x
Multiply 26 and 7 to get 182.
2288x=18\times 28x
Combine 2106x and 182x to get 2288x.
2288x=504x
Multiply 18 and 28 to get 504.
2288x-504x=0
Subtract 504x from both sides.
1784x=0
Combine 2288x and -504x to get 1784x.
x=0
Product of two numbers is equal to 0 if at least one of them is 0. Since 1784 is not equal to 0, x must be equal to 0.