How do you solve $\frac{x + 5}{x - 4} \leq 0$ $(x+5)/(x-4)<=0$ ?

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Answer 1 · 2018-06-10T17:24:14

$[- 5, 4)$ $[-5,4)$

Two equations can be formed from this:

$x + 5 \leq 0$ $x+5<=0$
and
$x - 4 \leq 0$ $x-4<=0$

Solve both to get

$x \leq - 5$ $x<=-5$ and $x \leq 4$ $x<=4$

however when $x = 4$ $x=4$ denominator is 0, and so makes the equation undefined, so $x < 4$ $x<4$

so the two ranges are

$- 5 \leq x < 4$ $-5<=x<4$ also written as $[- 5, 4)$ $[-5,4)$

How do you solve x+5x−4≤0(x+5)/(x-4)<=0?