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# Interesting questions from a student

Q: Why do we need to study inequality equations and solve those inequality questions? We don't go to open a shop to sell stuffs. We never use this in our life.

A: I never use inequality equations in my life either! BUT it proved that I may have more than one combination to get things DONE! Most importantly...it tests your "learning" ability for when you go to college.

### Comments

But you really use inequalities all of the time. If your family is splitting a pizza, then x+y+z <= 12 slices. If you are driving down the road, you have <=350 miles before you start pushing the car. There are a lot of practical examples where you can use inequalities. :)
Any subject can test one's learning ability but it sure can be frustrating to learn subjects if you suspect you will never make use of your efforts. But always try your best because you have a long life to live (I hope) and in such a long time you can often be taken surprise when something you have learned helps you, either directly, or indirectly by its similarity or other effect on your thinking. Brad's given some great examples, and this question I have also encountered a practical use for inequality equations. By the way, do you agree that these things should perhaps be called "inequations", since the word "equations" seems to imply equality? My memory brought me back to when I faced what was at the time a challenging problem in a lab portion of my second year of the study of electrical engineering, I had to design a simple dc power supply and the value for a certain resistor had to selected such that it would satisfy opposing design constraints, which were best expressed as inequalities. One was because the maximum power which would be absorbed by a zener diode had to be kept less than or equal to rating specified by the manufacturer, or I would end up "letting the smoke out of the circuit", in other words, boom! By the way, the power absorbed by the diode had an inverse relationship to the resistor value. The other constraint was the amount of voltage ripple in the output waveform under load (which had a direct relationship to the resistor size) had to be kept below an acceptable maximum value. By solving the two conflicting inequality expressions for the resistor value, I was able to discover the acceptable range of resistor values to meet both constraints. The nice thing about following this process was that if the circuit design was impossible, the conflicting results would reveal the untruth directly. for example if solving the first inequality gave the result that R had to be greater or equal to 100 ohms, but the second inequality gave a result that R had to be less than or equal to 50 ohms, it would be obvious that the circuit topology was not able to meet both constraints. Having determined the acceptable range (and fortunately, that the circuit topology was feasible) the actual value I picked was based on judgment of which inequality was more important for my design, keeping in mind the resistor-value-range that had been laid down by the existing constraints. Overall, solving the inequalities was a much quicker and more intuitive approach then the best alternative, which would have been repeatedly guessing resistor value and then working the inequality expressions to see if either of the constraints were violated. While not everyone wants to be an engineer, hopefully your student can extrapolate from this situation to ponder the possibility that inequalities can be useful whenever you know something about the maximum or minimum value of something that is acceptable to you, but either haven't decided or don't know exactly which precise value to use.

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