How do you know when to use brackets on rational equations in algebra?

Question

example would be

x+4/x-6 is less then or equal to 0

well i get the answer as (-4,6) but i know the need for brackets is in there because its an equal to question, which number do you know to put the bracket on or is it both? please help and thanks!

Answer 1

u mean like [x+4]/[x-6] the brackets r to separate them

if u had x + 4 and x-6 are separate equations and need brackets, without the brackets the problem could be interpreted in different ways

for example like someone might see it as 4/x + x - 6 which is not the original equation

Answer 2

this looks like
x + 4/x - 6 <= 0
so you can see its misleading without brackets
what are you referring to as brackets, parentheses or absolute value signs?
try (x + 4) / (x - 6) <= 0
you don't want x = 6 either because 6 - 6 = 0 and you don't want this in the denominator...you would be dividing by 0
x = -4 gives a zero value okay
so x <= -4 and that's it hope you see the brackets (parentheses) concept and the fact that x cannot equal 6

Answer 3

Brackets mean it includes the number.

So Your answer would actually be written as

[-4,6)

-4 will give you 0 which equals zero which is less than OR EQUAL to 0

6 will give you an undefined answer so thats why we use the parentheses on the 6

Answer 4

Sorry, ms. cookie, but I don't think you have done the problem correctly. You would do well to put brackets around the two terms to resolve ambiguity. So you would have (x+4)/(x-6) <= 0. Remember, any negative number, no matter how absolutely big it is, meets this criteria. Since the denominator goes to zero when x=6, the domain is from -infinity to <+6

Answer 5

x + 4/x - 6 <= 0

As written, the logical interpretation is

x + (4/x) - 6 <= 0

but you probably mean

(x + 4)/(x - 6) <= 0

This is still an inequality in spite of the = sign