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3x-2\left(x-7\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+14\geq 6
Use the distributive property to multiply -2 by x-7.
x+14\geq 6
Combine 3x and -2x to get x.
x\geq 6-14
Subtract 14 from both sides.
x\geq -8
Subtract 14 from 6 to get -8.