Question

Please help!
x+2 / -x-6 >0
write answer using interval notation.

Answer 1

Is it \[ \frac{x+2}{-x-6} > 0 \]

Answer 2

ya

Answer 3

If a / b > 0 (meaning positive) then:
either both a and b are positive OR
both a and b are negative.

Answer 4

x + 2 > 0 AND -x - 6 > 0
OR
x + 2 < 0 AND -x - 6 < 0

Solve x + 2 > 0 AND -x - 6 > 0 first. What do you get?

Answer 5

x>-2 and x>6

Answer 6

is that correct or did i misunderstand what i needed to do?

Answer 7

x + 2 > 0 AND -x - 6 > 0
x + 2 > 0
add -2 to both sides:
x > -2

-x - 6 > 0
add x to both sides:
-6 > x or x < -6

x > -2 AND x < -6
This is not possible. If x is less than -6 it cannot also be greater than -2. So no solution for this case.

The next case is: x + 2 < 0 AND -x - 6 < 0.
Try solving this case.

Answer 8

x<-2 and x>-6
that works i think?

Answer 9

Correct. x < -2 AND x > -6
In interval notation: (-6, -2).
Parenthesis because the end points are NOT included in the solution.

Answer 10

thanks so much for teaching me this.
So interval notation means the two numbers in the parenthesis?

Answer 11

Yes. If the solution for x is: (a,b) it means x > a AND x < b or simply a < x < b.
Here we use parenthesis and so the endpoints, a and b, are not included in the solution.

If the solution had been: \(-6 \le x \le -2\) then the solution would have been: [-6, -2] where we use brackets [ ] to include the endpoints in the solution.

But here it should be parenthesis: (-6, -2)

Answer 12

Solution is: [a, b] means \(a \le x \le b\).

Solution is: (a, b) means \(a \lt x \lt b\).

Answer 13

Thank you for your help!! Greatly appreciated

Answer 14

You are welcome.