I have been trying to solve the following inequality.(adsbygoogle = window.adsbygoogle || []).push({});

Solve the equation:

(2x+3)/(x-5)<¦(4x+12)/(x+1)¦

(where ¦¦ is meant to be modulus)

I tried to solve this, firstly by using the positive modulus:

(2x+3)/(x-5)<(4x+12)/(x+1)

which gives me two solutions:-

1) x< (13-SQRT(673))/4

and

2) x> ((13+SQRT(673))/4

I then tried to solve

(2x+3)/(x-5)>(-4x-12)/(x+1)

from which I got the following 2 solutions:-

3) (1+3SQRT(17))/4

and

4) (1-3SQRT(17))/4

If I sketch a graph of the equations, I can see that

x < (13-SQRT(673))/4

and

x > (13+SQRT(673))/4

are solutions, and also

(1-3SQRT(17))/4 < x < 5

where there is an asymptote (x = 5) for the LHS linear equation.

My question is have I used the right method in solving this type of inequality, and if so how do I disregard my result for (1+3SQRT(17))/4 and how should I treat the asymptote at x=-1 for the RHS equation.

Thanks

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# Homework Help: Solving Linear Equality with Modulus

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