Solve for x
x=2
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\left(x-1\right)\times 8=\left(3x-2\right)\times 2
Variable x cannot be equal to any of the values \frac{2}{3},1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(3x-2\right), the least common multiple of 3x-2,x-1.
8x-8=\left(3x-2\right)\times 2
Use the distributive property to multiply x-1 by 8.
8x-8=6x-4
Use the distributive property to multiply 3x-2 by 2.
8x-8-6x=-4
Subtract 6x from both sides.
2x-8=-4
Combine 8x and -6x to get 2x.
2x=-4+8
Add 8 to both sides.
2x=4
Add -4 and 8 to get 4.
x=\frac{4}{2}
Divide both sides by 2.
x=2
Divide 4 by 2 to get 2.
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