How do you solve $((x+7)(x-3))/(x-1)>=0$ ?

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How do you solve $((x+7)(x-3))/(x-1)>=0$ ?

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Answer 1 · 2017-02-03T15:23:34

The answer is $x in [-7,1 [ uu [3,+oo[$

Explanation:

Let $f(x)=((x+7)(x-3))/(x-1)$

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

Now we can build the sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaa)$ $-7$ $color(white)(aaaaaaa)$ $1$ $color(white)(aaaaaa)$ $3$ $color(white)(aaaaaa)$ $+oo$

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

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

$color(white)(aaaa)$ $x-3$ $color(white)(aaaaa)$ $-$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $||$ $color(white)(aa)$ $-$ $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $f(x)$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaa)$ $+$ $color(white)(aaaa)$ $||$ $color(white)(aa)$ $-$ $color(white)(aaaa)$ $+$

Therefore,

$f(x)>=0$ when $x in [-7,1 [ uu [3,+oo[$

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How do you solve $((x+7)(x-3))/(x-1)>=0$ ?

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How do you solve ((x+7)(x-3))/(x-1)>=0((x+7)(x-3))/(x-1)>=0?

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How do you solve $((x+7)(x-3))/(x-1)>=0$ ?