can someone help???
How many integer solutions has the inequality:x/x+4

Question

can someone help???
How many integer solutions has the inequality:x/x+4<=1/x+1

solomonzelman · Answer

$\huge\color{blue}{   \frac{x}{x+4} ≤  \frac{1}{x+1}}$

solomonzelman · Answer

cross multiply 
                 •••••

$\Large\color{blue}{   x(x+1) ≤  1(x+4)}$

$\Large\color{blue}{   x^2+x ≤  x+4}$

$\Large\color{blue}{   x^2 ~≤ ~ 4}$

$\Large\color{blue}{   x^2-4 ~~≤ 0}$

$\Large\color{blue}{   (x-2)(x+2)≤  0}$

solomonzelman · Answer

can you finish the problem off?

salazarblack · Answer

i found 2 solutions -2 and 2 ..but i don't know how to find the other 3

salazarblack · Answer

i got till that point as well..

solomonzelman · Answer

yes, so now we are getting

x ≤ 2           and       x≤ -2

solomonzelman · Answer

how many integers are there that are less than -2 ?

salazarblack · Answer

-3,-4,-5 and so on XD

anonymous · Answer

You should have $-2\le x\le2$ as a solution set, not $x\le-2$. The zero product property doesn't work for inequalities.

solomonzelman · Answer

didn't know that zero product prop. doesn't work for.....

anonymous · Answer

Also, note that $x=-1$ and $x=-4$ give undefined expressions, so know to avoid those.

anonymous · Answer

@SolomonZelman, polynomial inequalities can be tricky. What I do is try to picture it (in this case, a parabola shifted down by 4), and see which interval(s) satisfy the inequality. For $x^2-4$, the parabola dips below the x-axis between -2 and 2.

salazarblack · Answer

so then the answers would be -2,-1,0,1 and 2

salazarblack · Answer

but how do i know if x is<= to some value or x=>.. ?