SOLUTION: Could someone please help me solve a rational inequality using the critical point method? 1/x+2>x+2. I know how to use the critical point method, but I am not sure how to get the

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Question 1020598: Could someone please help me solve a rational inequality using the critical point method? 1/x+2>x+2. I know how to use the critical point method, but I am not sure how to get the problem in the correct form first? I appreciate any help you can give me!
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39623)   (Show Source): You can put this solution on YOUR website!
Make it into relation to zero.















Multiply left and right members by and REVERSE the direction of the inequality symbol...

-------this is the form which you analyze.

Continue with factorization.

The critical values of x are -1, -2, -3.
Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

Could someone please help me solve a rational inequality using the critical point method? 1/x+2>x+2. I know how to use the critical point method, but I am not sure how to get the problem in the correct form first? I appreciate any help you can give me!
, with 

1 = (x + 2)(x + 2) ---- Multiplying each side by LCD, x + 2, and changing INEQUALITY to equality



 --------- Subtracting 1 from each side

 --------- Reversing sides

(x + 3)(x + 1) = 0

x + 3 = 0         OR       x + 1 = 0

x = - 3           OR       x = - 1 



Thus, the 3 CRITICAL points are: - 2, - 3, and - 1. Arranged in numerical order, this

becomes: - 3, - 2, - 1. From these 3 CRITICAL points, the following 4 intervals have to be tested:

      x < - 3, or x = - 4

- 3 < x < - 2, or x = - 2.5

- 2 < x < - 1, or x = - 1.5

      x > - 1, or x = 0 

When the above intervals are tested, we find that: , are TRUE, and so, these are the solutions. 

The other 2 intervals make the INEQUALITY false, so they're not solutions. 

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