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2\left(x-1\right)+3\left(x-5\right)=1
Multiply both sides of the equation by 6, the least common multiple of 3,-2,6.
2x-2+3\left(x-5\right)=1
Use the distributive property to multiply 2 by x-1.
2x-2+3x-15=1
Use the distributive property to multiply 3 by x-5.
5x-2-15=1
Combine 2x and 3x to get 5x.
5x-17=1
Subtract 15 from -2 to get -17.
5x=1+17
Add 17 to both sides.
5x=18
Add 1 and 17 to get 18.
x=\frac{18}{5}
Divide both sides by 5.