Question

Identify the solution of this inequality
x+4/ x-8 is greater than/ equal to 0

Answer 1

x>8 U x<=-4

Answer 2

how would you solve for "x" say => \(\cfrac{x+4}{x-8} = 0\)

Answer 3

x=-4 and x=8

Answer 4

our answer choices are 8 or none of the above

Answer 5

hmm not sure on the x = 8, if you cross multiply, the x-8 goes poof
and all you're left with is x+4 which gives you x =-4

well, on an inequality is more or less the same

so the inequality will be
\(\bf x \ge -4\)

Answer 6

How about this one. 4x+3 / x-5. What do we do with the 4x+3?

Answer 7

so let's try using 8
x = 8
\(\bf 8 \ge -4\)
so that's true and is valid HOWEVER
remember the original equation was => \(\bf \cfrac{x+4}{x-8} = 0\)
if we use x = 8
that makes the denominator 8-8 = 0
and a fraction with a denominator of 0 is undefined, so we have that restriction

Answer 8

so x has to be greater than 8, or less than 8, but can't be 8, because we end up with an undefined expression

now if we use x = -4, then look at the numerator
x + 4, x = -4 => -4 + 4 = 0

0/WHATEVER = 0, and that's equal to 0, so that's ok
if you go below -4, you'd get a negative number in the numerator and positive in the denominator

that yields a negative fraction, which is not greater than or equal to 0

Answer 9

so based on the restrictions, "x" has to be greater than -4 but not 8
\(\bf x>-4; \ \ x \ne 8\)

Answer 10

I think X > -4 will not work...try putting x =-3 and check your solution

Answer 11

\(\bf \cfrac{-3+4}{-3-8} \implies \cfrac{1}{-11} \lt 0\)

Answer 12

true

Answer 13

I gather then that x has to be greater than or equal to 0, but not 8

Answer 14

The correct solution for this problem is
X <=-4 Union x>8
Let me know if anyone needs a detailed solution

Answer 15

\(\bf \bf x \ge 0; \ \ x \ne 8\)

Answer 16

hmmm, now that I think about it, the I have a -8 in the denominator :(

yes you're right @ankit042

Answer 17

so there @sherifoster , as @ankit042 originally said, yeah, based on the restrictions it has to be that \(\bf x \le -4 \cup x > 8\)

Answer 18

if you use something like -5 -7 .... the numerator becomes negative, so does the denominator and thus the fraction will be positive and greater than 0

if you use a value greater than 8, both numerator and denominator's are positive and that 's greater than 0

any value in between those 2 intervals, will give use either undefined at 8, or a negative atop or bottom, any negative rational is of not greater or equal to 0