Question

how is this solved ?

|2x +3| -9 ≤ 2

Answer 1

First add 9 to both sides ^.^

Answer 2

|2x +3| ≤ 2 +9
ok

Answer 3

|2x +3| ≤ 11
Which could mean either
2x +3 ≤ 11
or
2x + 3 ≥ -11

Answer 4

| means what | ?

Answer 5

|| means absolute value
Or, it just turns negative things positive
or, it turns positive things... still positive
HAHA
^.^

Answer 6

so |expression| ≤ - other expression
or
| expression | ≤ + other expression ?

Answer 7

ok , i do not understand why it changes what is outside of the ||

Answer 8

|expression| ≤ something
Just means
expression ≤ something
AND
expression ≥ negative something

Notice that I already removed the ||

Answer 9

oh , you also changed the sign from ≤ to ≥

Answer 10

Yeah, I did, didn't I? ^_^

Answer 11

what about something like this ?

|k-8|
------ > -4
8

Answer 12

should be fine, you can multiply 8 on both sides of the inequality without any worries :D
the problems come when you multiply something negative on both sides... then that means you also have to switch the > to a <

Answer 13

ok, so the absolute value only changes the other side of the inequality because it (itself) can only be positive. thus the sign changes direction when the absolute value represents negative or positive. therefor, everything not with in the |abs| must be moved to the other side for this to work. correct ?

Answer 14

Yeah

Answer 15

sweet . thanks :)