Question

solve abs(2x+6)>= abs(9x-8), answer in interval form

Answer 1

\(\large\color{blue}{ \left| 2x+6 \right|= \left| 9x-8 \right| }\) should be converted to, \(\large\color{blue}{ 2x+6 =\pm( 9x-8 ) }\).

Answer 2

where you would have 2 solutions for x.

Answer 3

are you sure about that?

Answer 4

\[|2x+6|=\begin{cases}
-2x+6\\
2x+6
\end{cases}\]

Answer 5

I am fairly sure.
Reason.
when you say that
a^2=b^2 (and this statement you can see when you complete the square)
you don't say that
+-a=+-b
No...
you just say
a=+-b

Answer 6

here, it is sort of the same.

Answer 7

ahh that gives me another idea

Answer 8

\[\sqrt{ 2x+6 } ^{ 2 } \ge\sqrt{ 9x-8 } ^{ 2 } \]

Answer 9

yeah, my sign was off, it should be \(\large\color{blue}{ \ge}\) but you got the idea of my first statement though.

Answer 10

nevermind im not sure how to get plus minus from this

Answer 11

well, you know that if \(\large\color{blue}{ \left| x \right|=a}\), then \(\large\color{blue}{ x=\pm a}\)

Answer 12

mm so i solved your \(\large\color{blue}{ 2x+6 =\pm( 9x-8 ) }\)

Answer 13

but it doesn't quite fit with the graph

Answer 14

neither does the answers at the critical points match

Answer 15

wait wait

Answer 16

nevermind it worked XD did bad math

Answer 17

im curious though about your example
a^2=b^2
becoming
\(a= \pm b\)