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

2 Answers
Nov 24, 2017

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)xcolor(white)(aaaa)-oocolor(white)(aaaaaa)-8color(white)(aaaaaaa)-6color(white)(aaaaa)+oo

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

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

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

Nov 24, 2017

( -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 )