absolute value..2 different answer

absolute value

I getting a different answer...don't know why

|3-4x|≥2

what i did was=====> i made it in to 2 parts ===>3 - 4x ≥ 2 and 3 - 4x ≥-2

my final answer that i got is

1/4≥x (first part) and (second part) 5/4 ≥ x

but the teacher got

1/4≥x and 5/4 ≤ x

why did the sign change for the last one? i dont get it

how to graph absolute value

how to graph this

y=3|x+2|-9

it says graph: vertex and intercepts

by the way how do u find the vertex of any problem?

thanks