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18=\left(3\times 26+1\right)x
Multiply both sides of the equation by 26, the least common multiple of 13,26.
18=\left(78+1\right)x
Multiply 3 and 26 to get 78.
18=79x
Add 78 and 1 to get 79.
79x=18
Swap sides so that all variable terms are on the left hand side.
x=\frac{18}{79}
Divide both sides by 79.