document.write( "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! \n" ); document.write( "

Algebra.Com's Answer #636468 by MathTherapy(10555) $\"\"$ $\"About$

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\n" ); document.write( "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!
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, with 
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document.write( "1 = (x + 2)(x + 2) ---- Multiplying each side by LCD, x + 2, and changing INEQUALITY to equality
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document.write( " --------- Subtracting 1 from each side
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document.write( " --------- Reversing sides
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document.write( "(x + 3)(x + 1) = 0
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document.write( "x + 3 = 0         OR       x + 1 = 0
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document.write( "x = - 3           OR       x = - 1 \r
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document.write( "Thus, the 3 CRITICAL points are: - 2, - 3, and - 1. Arranged in numerical order, this
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document.write( "becomes: - 3, - 2, - 1. From these 3 CRITICAL points, the following 4 intervals have to be tested:
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document.write( "      x < - 3, or x = - 4
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document.write( "- 3 < x < - 2, or x = - 2.5
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document.write( "- 2 < x < - 1, or x = - 1.5
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document.write( "      x > - 1, or x = 0 
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document.write( "When the above intervals are tested, we find that: , are TRUE, and so, these are the solutions. 
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document.write( "The other 2 intervals make the INEQUALITY false, so they're not solutions. \n" );
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