Question

solve 2x - 4/ x +1 > 0

Answer 1

You may simplify this problem for yourself and others if you'd please use ( ) to group terms in the numerator and the den. together.

For example, do you mean 2x - 4/x +1 > 0, or do you mean

(2x-4) / (x+1) ?

This is really important as you try to convey math symbolism accurately to others.

Answer 2

2x - 4/x +1 > 0,

Answer 3

the first equation u mentioned

Answer 4

it it this
\[ \frac{2x-4}{x+1} > 0 \]?

Answer 5

yes exactly

Answer 6

exactly as username "phi" has it

Answer 7

So, those parentheses make all the difference in the world.

Looking at phi's inequality:

for which x value is the rational function undefined?
For which x value is the numerator of this fraction = to 0?

Answer 8

ok, that means if you type it in, you should use parens, and it would look like this
(2x-4) / (x+1) > 0

Or , use the equation editor (see the button on the lower left of where you input )

Answer 9

\[2x-\frac{4}{x}+1>0\] or \[\frac{2x-4}{x+1}>0\]

Answer 10

the second equation tomhue

Answer 11

to answer the question, notice that if the top is positive and (at the same time) the bottom is positive, the quotient is positive. And positive means > 0

OR
if both the top and bottom are negative (at the same time) the quotient will be positive (meaning > 0)

Answer 12

Can you figure out what values make x+1 > 0 true ?

Answer 13

I solved the equation and ended up with x = -1 and x = 2, so now I am trying to write it out as an equation. I know has has to be greater than 2 but it can also be less than -1, like -4...

Answer 14

finding x= -1 and x=2 is helpful. But we have to think about it.

First, do you agree that if the top number is positive and the bottom number is positive , then the result will be positive ?

Answer 15

yes

Answer 16

and do you agree that positive number is > 0
?
I assume you think so.

you found that the top 2x-4=0 when x is 2
if x is bigger than 2, then 2x-4 will be bigger than 0. i.e. 2x-4 will be positive.
the bottom x+1 will also be positive

in other words, if x>2 then (2x-4) is positive and x+1 is positive and the result is positive .

one way for (2x-4)/(x+1) > 0 to be true is for x > 2

Answer 17

ok makes sense

Answer 18

you also found x+1=0 when x = -1

if x is less than -1, x+1 will be negative.
the top
2x - 4 with x < -1 will also be < 0

when the top is negative, and the bottom is negative
(2x-4)/(x+1) will be positive (negative divided by negative is positive)

so another way for
(2x-4)/(x+1) > 0 is when x < -1

Answer 19

and just to finish off the thought, if x is bigger than -1 but less than 2
the top will be negative and the bottom will be positive, and the result of negative divided by positive will be negative... meaning (2x-4)/(x+1) < 0
(which we do not want)

Answer 20

ok, so what is the final answer?

Answer 21

Hope you won't object to my presenting a different approach, one based on phi's work.

Earlier I asked you to tell me what x value makes the numerator = 0, and I also asked you which x value makes the den. = 0. Those values are 2 and -1 respectively. (BRB)

Answer 22

Graph these critical numbers on a number line as follows. Then identify the intervals defined by those 2 critical numbers: