Solve (- x - 7)/(x + 2) < 0 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{-x-7}{x+2}<0$$

Solve for x

$x\in \left(-\infty,-7\right)\cup \left(-2,\infty\right)$

Solution Steps

For the quotient to be negative, $-x-7$ and $x+2$ have to be of the opposite signs. Consider the case when $-x-7$ is positive and $x+2$ is negative.

$$-x-7>0$$ $$x+2<0$$

The solution satisfying both inequalities is $x<-7$.

$$x<-7$$

Consider the case when $x+2$ is positive and $-x-7$ is negative.

$$x+2>0$$ $$-x-7<0$$

The solution satisfying both inequalities is $x>-2$.

$$x>-2$$

The final solution is the union of the obtained solutions.

$$x<-7\text{; }x>-2$$