Can anyone help with this rational inequality

7/(x+1)>7

I think its zero but apparently the real answer is -1<x>0. (Cool)

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- Dec 12th 2010, 03:32 PMhomeylova223Rational inequality?
Can anyone help with this rational inequality

7/(x+1)>7

I think its zero but apparently the real answer is -1<x>0. (Cool) - Dec 12th 2010, 03:36 PMPlato
- Dec 12th 2010, 03:38 PMArchie Meade
- Dec 12th 2010, 03:43 PMsnowtea
The first thing we all want to do is multiply both sides of the inequality by (x+1), but we need to be careful because the inequality changes if we multiply by a negative value, so 2 cases:

Case 1) x+1 < 0 or x < -1

Then 7 < 7(x + 1) and 7 < 7x + 7 and we get x > 0

so taking all the conditions, we have x < -1 and x > 0, but this is not possible, so case 1 gives no solutions

Case 2) x + 1 > 0 or x > -1

Then 7 > 7(x+1) and 7 > 7x + 7 and we get x < 0

so taking all the conditions we have x > -1 and x < 0, this is a range and can be written as -1 < x < 0 - Dec 12th 2010, 03:58 PMSoroban
[soze=3]Hello, homeylova223![/size]

Quote:

. WHAT is zero?

We have: .

Divide by 7: .

Then we have: .

Multiply by -1: .

If a fraction is negative: the numerator and denominator have opposite signs.

. . . This says: .**and**. . . impossible

. . . This says: . and

This is possible: .

- Dec 12th 2010, 03:59 PMSoroban
Hello, homeylova223!

Quote:

. WHAT is zero?

We have: .

Divide by 7: .

Then we have: .

Multiply by -1: .

If a fraction is negative: the numerator and denominator have opposite signs.

. . . This says: .**and**. . . impossible

. . . This says: . and

This is possible: .