Question

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

1/(8+ x)<_(8-5x)/43

Answer 1

(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

Answer 2

been a while could be wrong >.<

Answer 3

ah i forget how to put it in interval notation

Answer 4

\[−7≤x≤\frac{3}{5} \text{ or } x<−8\]

Answer 5

gotta teach me Zarkon

Answer 6

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

Answer 7

\[1/(8+ x)\le(8-5x)/43\]

write as

\[0\le(8-5x)/43-1/(8+ x)\]

then write the RHS as one fraction

Answer 8

Zarkom so how do I write it in interval notation?

Answer 9

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