When multiplying one side of an inequality with a positive number it's important to multiply the other side by the same number to ensure that the inequality still holds. For example, the inequality 0.2x≤2 can be multiplied by 5 on both sides.
5⋅0.2x≤5⋅2⇔x≤10
However, this only yields when multiplying by positive numbers. When multiplying both sides by a negative number the inequality sign must be flipped.
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