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Word Problems

Word Problems

Inequalities

We have four possible inequality signs to choose from: <, >, ≤, and ≥. There is also the slightly less popular ^, which means that everything below is greater than everything above, but that brings us into a touchy area, spiritually speaking. Translating English into one of these symbols is a matter of common sense. Good thing you have some of that.

The signs < and > are usually straightforward.

  • "Three is less than x'' can be abbreviated by 3 < x.
     
  • "5 is more than x'' can be written in symbols as 5 > x.

When we're translating into statements that use ≤ or ≥, we have a slightly wider range of English phrases to use. For example, each of the following English statements translates into symbols as x ≤ 20.

  • x is less than or equal to twenty.
     
  • x is at most twenty.
     
  • x is not more than twenty.
     
  • x is not greater than twenty.
     
  • Twenty could be more than x, could be exactly as much as x. You'll never know. Na-nana-boo-boo.

Each of these following English statements translates into symbols as x ≥ 0.

  • x is greater than or equal to zero.
     
  • x is not less than zero.
     
  • x is not smaller than zero.
     
  • x is at least zero.
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