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x+5x\geq 0
Multiply both sides of the equation by 5. Since 5 is positive, the inequality direction remains the same.
6x\geq 0
Combine x and 5x to get 6x.
x\geq 0
Product of two numbers is ≥0 if both are ≥0 or both are ≤0. Since 6\geq 0, x must be ≥0.