How do you solve $(x+26)/(x+5)>=0$ ?

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Answer 1 · 2016-08-06T07:01:37

$x in (-oo, -26] uu (-5, oo)$

If $x=-5$ then the denominator of the rational expression is zero and the quotient is undefined. So $-5$ is not part of the solution set.

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Case $bb(x < -5)$

If $x < -5$ then $(x+5) < 0$

Multiply both sides of the inequality by $(x+5)$ and reverse the inequality (since $(x+5) < 0$ ) to get:

$x+26 <= 0$

Subtract $26$ from both sides to get:

$x <= -26$

So $(-oo, -26]$ is part of the solution set.

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Case $bb(x > -5)$

If $x > -5$ then $(x+5) > 0$

Multiply both sides of the inequality by $(x+5)$ to get:

$x+26 >= 0$

Subtract $26$ from both sides to get:

$x >= -26$

Since $x > -5$ this is already true.

So $(-5, oo)$ is part of the solution set.

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Conclusion

The solution set is:

$(-oo, -26] uu (-5, oo)$

How do you solve (x+26)/(x+5)>=0(x+26)/(x+5)>=0?