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

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

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Answer 1 · 2016-09-23T13:07:37

The solution for the inequality is $-2 < x < 1$

Explanation:

As $(x-1)/(x+2)<0$ , $x$ cannot take value of $-2$ .

From this we know that the product $(x-1)/(x+2)$ is negative. It is apparent that sign of binomials $(x+2)$ and $x-1$ will change around the values $-2$ and $1$ respectively. In sign chart we divide the real number line using these values, i.e. below $-2$ , between $-2$ and $1$ and above $1$ and see how the sign of $(x-1)/(x+2)$ changes.

Sign Chart

$color(white)(XXXXXXXXXXX)-2color(white)(XXXXX)1$

$(x+2)color(white)(XXX)-ive color(white)(XXXX)+ive color(white)(XXXX)+ive$

$(x-1)color(white)(XXX)-ive color(white)(XXXX)-ive color(white)(XXXX)+ive$

$(x-1)/(x+2)color(white)(XXX)+ive color(white)(XXX)-ive color(white)(XXXX)+ive$

It is observed that $(x-1)/(x+2) < 0$ between $-2$ and $1$ i.e. $-2 < x < 1$ , which is the solution for the inequality.

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

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Explanation:

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