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The best point to check (inequalities)

  • Writer: Tom Keeler
    Tom Keeler
  • Jan 23
  • 1 min read

What is the best point to check to decide whether to fill in to the left or right of the solution point? For example, if I have to make at least $120 to fund my "Let's Make Math Optional" Facebook campaign, I can make $10/hr and I already have $20, how many hours do I have to work. The inequality would be 10x+20>= 120. You figure out that if x=10, you'll have exactly $120. So you put a solid dot at 10. Does the arrow to to the left towards zero or to the right, towards positive infinity? In this case, it is intuitively clear, because you want to make a lot of money, so bigger is better. But a good practice is to ask if 0 is part of the solution. 10*0 + 20 = 20 is clearly not part of the solution. So you know to draw the solution arrow to the right from 10 not to the left, which would include 0.

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