Question

|3x − 6| > 3?
I know that you must separate it into two separate inequalities one equaling a positive and one equaling a negative, but would you also change the greater than symbol to a lesser than symbol when you solve the negative?

Answer 1

yes
|a|>b

then we have
a>b
a<-b

Answer 2

so you have the two equations
3x-6>3
and
3x-6<-3

Answer 3

ty :)

Answer 4

that and should say or

Answer 5

here is one way to think of it
|3x − 6| > 3

if the stuff inside is positive, you can drop the absolute value,
3x - 6 > 3

if the stuff inside is negative, the absolute value does the same thing as multiplying by -1 (-1 times a negative gives you a positive)
-1(3x-6) > 3
distribute the -1:
-3x + 6 > 3
add 3x to both sides
6 > 3 +3x
subtract 3 from both sides
3 > 3x
or
3x < 3

Answer 6

should that not say -3x + 6 < 3
@phi?

Answer 7

to quote zzr
3x-6>3
and
3x-6<-3

the last is the same as 3x < 3

Answer 8

I've actually done that in certain situations and it becomes easier. :)

Answer 9

the trick with > or < is always add or subtract from each side
that way you don't have to remember to switch the order of the < or >

(multiplying by -1 means you have to switch the order of the > or <)

so
-x > 2
you can multiply by -1 and swap > to <
x < -2

or you can add x to both sides
0 > x+2
then add -2 to both sides
-2 > x
or
x < -2
the point is adding gets you the correct > or <

on the other hand, remembering the shortcuts is faster...