How do you solve $(x-1)(3x-4)>=0$ using a sign chart?

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Answer 1 · 2016-12-06T08:32:52

The answer is $x in ] -oo,1 ] uu [ 4/3, +oo[$

Let $f(x)=(x-1)(3x-4)$

Let's do the sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaa)$ $1$ $color(white)(aaaa)$ $4/3$ $color(white)(aaaa)$ $+oo$

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

$color(white)(aaaa)$ $3x-4$ $color(white)(aaaa)$ $-$ $color(white)(aaa)$ $-$ $color(white)(aaaa)$ $+$

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

So, $f(x)>=0$ for $x in ] -oo,1 ] uu [ 4/3, +oo[$

graph{y=(x-1)(3x-4) [-1.863, 3.006, -1.232, 1.2]}

How do you solve (x-1)(3x-4)>=0(x-1)(3x-4)>=0 using a sign chart?