SOLUTION: I. Why must we reverse the direction of the inequality sign change when both sides are multiplied or divided by a negative number? (please note: we already know the answer will be
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Question 425344: I. Why must we reverse the direction of the inequality sign change when both sides are multiplied or divided by a negative number? (please note: we already know the answer will be wrong if we don’t – but why is this the case?)
II. Does this happen with equations? Why or why not?
III. Write an inequality for your classmates to solve. In your inequality, use both the multiplication and addition properties of inequalities.
IV. Consider solving your classmates’ inequality. Explain how you arrived at your answers. Also, help other students who may be having difficulty solving inequalities. Ask clarifying questions if your need additional assistance.
You can put this solution on YOUR website! If we can say that , guaranteed. We can subtract both sides by x to obtain , which implies by the symmetric property. In general, we can multiply by some positive constant k, i.e. .
