Question

ok so i have this question (x+2)/(x-7) <= 0. why is the result [-2,7) and NOT [-2,7]??

Answer 1

because you cannot divide by zero

Answer 2

i tried it once, had a headache for like two weeks

Answer 3

\(x\) CAN be \(-2\) because \[\frac{-2+2}{-2-7}=\frac{0}{-9}=0\] a perfectly good number

Answer 4

I know that signs that look like this\[\le or \ge \] are a closed circle and a bracket. so why is it one parenthesis and ALSO a bracket

Answer 5

but \(x\) CANNOT be \(7\) because \[\frac{7+2}{7-7}=\frac{9}{0}\] which is NOT a number

Answer 6

\[[-2,7]\]includes the number 7, but you cannot replace x by 7

Answer 7

\[[-2,7)\]does NOT include the number 7, and that is good, because 7 is out

Answer 8

So, @satellite73 , if i take the numbers and plug them in and get a REAL working number then its a bracket. If it's not a real number its a parenthesis. Correct?

Answer 9

i suppose you can think of it that way
what you have to make sure of is that you don't get a zero in the denominator

Answer 10

SO.....if it's a zero in the denominator with that number, it's a parenthesis.

Answer 11

@satellite73

Answer 12

yes

Answer 13

if i plug a number in for x and it gives me a zero in the denominator then it will be a parenthesis. PERFECT thank you for that

Answer 14

yw

Answer 15

does the sign in the equation mean anything to me then as long as that rule works??? @satellite73

Answer 16

[-2,7] is incorrect because it INCLUDES 7, so the denominator (x-7) would be zero. Div. by zero is not defined.

Thus, you must restrict the domain to [-2,7) ... this does NOT include 7 and we do NOT have div. by zero. OK?