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3\left(1\times 2+1\right)x\geq 10
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.
3\left(2+1\right)x\geq 10
Multiply 1 and 2 to get 2.
3\times 3x\geq 10
Add 2 and 1 to get 3.
9x\geq 10
Multiply 3 and 3 to get 9.
x\geq \frac{10}{9}
Divide both sides by 9. Since 9 is positive, the inequality direction remains the same.