How do you solve $\frac{x - 7}{x - 1} < 0$ $(x-7)/(x-1)<0$ ?

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Answer 1 · 2017-05-17T05:02:46

The solution is $x \in (1, 7)$ $x in (1,7)$

Let $f (x) = \frac{x - 7}{x - 1}$ $f(x)=(x-7)/(x-1)$

The domain of $f (x)$ $f(x)$ is $D_f(x)=RR-{1}$

We build a sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaaaa)$ $1$ $color(white)(aaaaaaaa)$ $7$ $color(white)(aaaa)$ $+oo$

$color(white)(aaaa)$ $x-1$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $||$ $color(white)(aaaa)$ $+$ $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $x-7$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $||$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $f(x)$ $color(white)(aaaaa)$ $+$ $color(white)(aaaa)$ $||$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $+$

Therefore,

$f(x)<0$ when $x in (1,7)$

How do you solve (x-7)/(x-1)<0x−7x−1<0(x-7)/(x-1)<0?