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When solving a problem involving money, a negative answer can represent an overdrawn account or an amount owed.
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A car requires 15 liters of petrol to travel 200 km.How much petrol is needed to travel 120 km?
"What is 3*(-5)" would be such a problem.
That depends on the type of problem. For example, if you have equations involving radicals, it often helps to square both sides of the equation. Note that when you do this, you may introduce additional solutions, which are not solutions to the original equation.