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114x+95x=30\left(1\times 19+1\right)
Multiply both sides of the equation by 570, the least common multiple of 5,6,19.
209x=30\left(1\times 19+1\right)
Combine 114x and 95x to get 209x.
209x=30\left(19+1\right)
Multiply 1 and 19 to get 19.
209x=30\times 20
Add 19 and 1 to get 20.
209x=600
Multiply 30 and 20 to get 600.
x=\frac{600}{209}
Divide both sides by 209.