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Solving Quadratic Inequalities

1ai. x^2 less than or equal to sign 8
1ei. (x-4)(x+1)>0

User Spiilmusic
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1 Answer

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20 votes

Answer:

1ai. x is less than or equal to 8

1ei. x > 4 and x > 1

Explanation:

Steps for solving 1ai

  1. Factor x² less then or equal to 8 you would do this by finding two numbers the product is equal to zero and the sum would equal to zero. You would find all factors that would equal to your terms like for example x² has the factors x•x and the factors of 0 are 0 so it would be (x+0)(x+0) is less than or equal to 8
  2. Split the factoed terms into two inequalities since you're dealing with polynomial inequalities you will either have one or more solutions. For example you will have to solve x + 0 is less than or equal to 8
  3. Solve for x by doing the inverse operation in this case the addition will become subtraction so it will be x + 0-0 is less than or equal to 8 - 0 which would be x is greater than or equal to 8

Steps to solve 1ei

  1. Split the factored terms into 2 inequalities so (x-4) (x+1) >0 will become x-4>0 and x+1>0
  2. Solve for x in this case x-4>0 will become x-4+4> 0+4 which is x>4 and x+1>0 will be x+1-1>0-1 which is x>-1
User Ifoma
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