OpenStudy (anonymous):

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

2 years ago
OpenStudy (aum):

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

2 years ago
OpenStudy (anonymous):

ya

2 years ago
OpenStudy (aum):

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

2 years ago
OpenStudy (aum):

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?

2 years ago
OpenStudy (anonymous):

x>-2 and x>6

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (aum):

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.

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (aum):

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

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (aum):

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)

2 years ago
OpenStudy (aum):

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

2 years ago
OpenStudy (anonymous):

Thank you for your help!! Greatly appreciated

2 years ago
OpenStudy (aum):

You are welcome.

2 years ago