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3\left(x-2\right)\geq 2\left(x-1\right)+7
Multiply both sides of the equation by 18, the least common multiple of 6,9,18. Since 18 is positive, the inequality direction remains the same.
3x-6\geq 2\left(x-1\right)+7
Use the distributive property to multiply 3 by x-2.
3x-6\geq 2x-2+7
Use the distributive property to multiply 2 by x-1.
3x-6\geq 2x+5
Add -2 and 7 to get 5.
3x-6-2x\geq 5
Subtract 2x from both sides.
x-6\geq 5
Combine 3x and -2x to get x.
x\geq 5+6
Add 6 to both sides.
x\geq 11
Add 5 and 6 to get 11.