How do you solve and write the following in interval notation: $(x + 6)(x + 8) ≥ 0$ ?

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How do you solve and write the following in interval notation: $(x + 6)(x + 8) ≥ 0$ ?

2 Answers

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Answer 1 · 2017-11-24T12:59:57

The solution is $x in (-oo,-8] uu [-6, +oo)$

Explanation:

Let $f(x)=(x+6)(x+8)$

Build a sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaaaa)$ $-8$ $color(white)(aaaaaaa)$ $-6$ $color(white)(aaaaa)$ $+oo$

$color(white)(aaaa)$ $x+8$ $color(white)(aaaaa)$ $-$ $color(white)(aaaa)$ $0$ $color(white)(aaaa)$ $+$ $color(white)(aaaaa)$ $+$

$color(white)(aaaa)$ $x+6$ $color(white)(aaaaa)$ $-$ $color(white)(aaaa)$ #color(white)(aaaaa)-# $color(white)(aa)$ $0$ $color(white)(aa)$ $+$

$color(white)(aaaa)$ $f(x)$ $color(white)(aaaaaa)$ $+$ $color(white)(aaaa)$ $0$ $color(white)(aaaa)$ $-$ $color(white)(aa)$ $0$ $color(white)(aa)$ $+$

Therefore,

$f(x)>=0$ when $x in (-oo,-8] uu [-6, +oo)$

graph{(x+6)(x+8) [-11.54, 0.947, -2.155, 4.09]}

Answer 2 · 2017-11-24T13:23:37

$( -oo, -8 ] uu [ -6, oo )$

Explanation:

enter image source here

$( x + 6 )$ is ZERO for $x = ( -6 )$

$( x + 6 )$ is POSITIVE for $x > ( -6 )$

$( x + 8 )$ is ZERO for $x = ( -8 )$

$( x + 8 )$ is POSITIVE for $x > ( -8 )$

Refer to the SIGN Table

Our required Interval Notation can be written as follows:

$( -oo, -8 ] uu [ -6, oo )$

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How do you solve and write the following in interval notation: $(x + 6)(x + 8) ≥ 0$ ?

2 Answers

Explanation:

Explanation:

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How do you solve and write the following in interval notation: $(x + 6)(x + 8) ≥ 0$ ?