How do you solve $(x-1)(x-2)(x-3)<=0$ using a sign chart?

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How do you solve $(x-1)(x-2)(x-3)<=0$ using a sign chart?

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Answer 1 · 2016-11-09T08:54:20

The answer is $x in ] -oo,1 ] uu [2, 3]$

Explanation:

Let $f(x)=(x-1)x-2)(x-3)$

Let's do the sign chart
$color(white)(aaaaa)$ $x$ $color(white)(aaaaa)$ $-oo$ $color(white)(aaaaa)$ $1$ $color(white)(aaaaa)$ $2$ $color(white)(aaaaa)$ $3$ $color(white)(aaaaa)$ $+oo$
$color(white)(aaaaa)$ $x-1$ $color(white)(aaaaa)$ $-$ $color(white)(aaaaa)$ $+$ $color(white)(aaaa)$ $+$ $color(white)(aaa)$ $+$
$color(white)(aaaaa)$ $x-2$ $color(white)(aaaaa)$ $-$ $color(white)(aaaaa)$ $-$ $color(white)(aaaa)$ $+$ $color(white)(aaa)$ $+$
$color(white)(aaaaa)$ $x-3$ $color(white)(aaaaa)$ $-$ $color(white)(aaaaa)$ $-$ $color(white)(aaaa)$ $-$ $color(white)(aaa)$ $+$
$color(white)(aaaaa)$ $f(x)$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaaa)$ $+$ $color(white)(aaaa)$ $-$ $color(white)(aaa)$ $+$

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How do you solve $(x-1)(x-2)(x-3)<=0$ using a sign chart?

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How do you solve (x-1)(x-2)(x-3)<=0(x-1)(x-2)(x-3)<=0 using a sign chart?

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How do you solve $(x-1)(x-2)(x-3)<=0$ using a sign chart?