Solve the following inequality and write your answer using interval notation. Please show all of your work.

1/(8+ x)

Question

Solve the following inequality and write your answer using interval notation. Please show all of your work.
 
1/(8+ x)<_(8-5x)/43

anonymous · Answer

(1/(8+ x)<_(8-5x)/43)43
(43/(8+x)<_(8-5x))(8+x)
43=(8-5x)(8+x)
43<_ 5x^2-32x+64
0<_5x^2-32x+21
0<_ (5x+3 )(x-7 )

x|x<_-3/5, 7

anonymous · Answer

been a while could be wrong >.<

anonymous · Answer

ah i forget how to put it in interval notation

zarkon · Answer

$$−7≤x≤\frac{3}{5} \text{ or } x<−8$$

anonymous · Answer

gotta teach me Zarkon

anonymous · Answer

im just glad i was headed in the right direction maybe lol

zarkon · Answer

$$1/(8+ x)\le(8-5x)/43$$

write as 

$$0\le(8-5x)/43-1/(8+ x)$$

then write the RHS as one fraction

anonymous · Answer

Zarkom so how do I write it in interval notation?

zarkon · Answer

$$(-\infty,-8)\cup [-7,3/5]$$