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What are the similarities and differences in solving equations and inequalities?

Git Gud
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Lee
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  • As far as difference is concerned, with an equation you can set cross products equals (and then solve) if exactly two fractional terms are seperated by an equal sign. With inequalities you can not do that. – imranfat May 16 '14 at 14:11

1 Answers1

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Similarities

  1. Adding or subtracting a number from both sides.
  2. Multiplying or dividing both sides by a positive number.
  3. Applying an increasing function to both sides.
  4. Simplifying one or both sides.

Differences

  1. Multiplying or dividing both sides by a negative number changes the direction of an inequality. So we cannot multiply or divide both sides by a variable unless we know that the variable is either always positive or always negative. This is not a concern when solving equalities.
  2. When applying a decreasing function to both sides of an inequality, the direction of the inequality changes.
  3. Swapping both sides of an inequality also changes the direction of an inequality. Again we don't have to worry about this with equalities.
k170
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