Question

Solve the nonlinear inequality. Express the solution using interval notation.

4x + 8 over/x − 6 < 0

Answer 1

\[\frac{4x+8}{x-6}<0\]

Answer 2

set the numerator = 0 and solve. you get
\[4x+8=0\]
\[4x=-8\]
\[x=-2\]

Answer 3

set the denominator = 0 and solve. you get
\[x-6=0\]
\[x=6\]

Answer 4

thats right

Answer 5

so your fraction will change sign at -2 and at 6

Answer 6

thats what i was getting. thanks

Answer 7

from
\[(\infty,-2)\] both top and bottom will be negative, and negative over negative is positive

Answer 8

so what does that look like on the number line

Answer 9

from
\[(-2,6)\] top will be positive but bottom negative and positive over negative is negative.

Answer 10

and from
\[(6,\infty)\] both will be positive. so you now know where this fraction is positive and where it is negative.

Answer 11

i am not sure what you are asking. what does it look like on a number line. some people draw this

Answer 12

like brackets or parentheses and which way is line

Answer 13

4x+8 ----------------(-2)++++++++++++++++++++++++++++++
x-6 ------------------------------------------------(6)+++++++++++++

fraction ++++++++(-2)-------------------------(6) ++++++++++++++

Answer 14

you want to know where it is negative. it is negative on the interval from -2 to 6

Answer 15

in interval notation it looks like
\[(-2,6)\]

Answer 16

as a picture on the number line it looks like

______________-2 ################ 6 ______________ where the shaded area is your solution