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3x-2\left(x-1\right)\geq 6
Multiply both sides of the equation by 6, the least common multiple of 2,3. Since 6 is positive, the inequality direction remains the same.
3x-2x+2\geq 6
Use the distributive property to multiply -2 by x-1.
x+2\geq 6
Combine 3x and -2x to get x.
x\geq 6-2
Subtract 2 from both sides.
x\geq 4
Subtract 2 from 6 to get 4.