painful question

[momomath]

Solve the Inequality:

8/(x+6) + 16/(x-8) < x + 3



I keep trying to get rid of the fractions, and I end up with 0 < x^3 + x^2 - 78x + 176 , but i I think that's wrong. And if it's right, I can't find a factor of it.

 

[DrPhil]

Solve the Inequality:

8/(x+6) + 16/(x-8) < x + 3



I keep trying to get rid of the fractions, and I end up with 0 < x^3 + x^2 - 78x + 176 , but i I think that's wrong. And if it's right, I can't find a factor of it.

You have to be extremely careful multiplying both sides of an inequality by a variable, because negative changes the sense. Therefore just combine the fractions on the left.

\(\displaystyle \displaystyle \dfrac{8(3x + 4)}{(x + 6)(x - 8)} < x + 3 \)

There are four values of x where one side or the other switches sign. You will probably have to treat (x+3)>0 separately from (x+3)<0.

 

[Deleted member 4993]

Solve the Inequality:

8/(x+6) + 16/(x-8) < x + 3



I keep trying to get rid of the fractions, and I end up with 0 < x^3 + x^2 - 78x + 176 , but i I think that's wrong. And if it's right, I can't find a factor of it.

per my calculation get


0 < x^3 + x^2 - 78x - 176

0<(x+8)(x² - 7x -22)

Be careful about ± signs - those flip the equality.