How do you solve the inequality $-x^2-6x+7<=0$ ?

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Answer 1 · 2017-01-02T07:38:53

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

Let`s rewrite the inequality

$x^2+6x-7>=0$

We factorise

$(x-1)(x+7)>=0$

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

The domain of $f(x)$ is $D_f(x)=RR$

We do a sign chart

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

$color(white)(aaaa)$ $x+7$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaaa)$ $+$ $color(white)(aaaaa)$ $+$

$color(white)(aaaa)$ $x-1$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaaa)$ $-$ $color(white)(aaaaa)$ $+$

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

Therefore,

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

How do you solve the inequality -x^2-6x+7<=0-x^2-6x+7<=0?