Question

Ix+3I<14

Answer 1

that means
x+3 < 14
or
-(x+3) < 14

the first relation can be written as x +3 -3 < 14 -3 (add -3 to both sides)
simplify (3-3 is 0) and 14-3 is 11 : x < 11

for the second relation, distribute the - sign: -(x+3) means -1*(x+3)
multiply -1 times each term in the parens: -x -3
so you now have -x -3 < 14
if you leave it -x we will eventually have to "flip" the < sign. It is safer to always add and if you have to divide by POSITIVE numbers. so add +x to both sides
+x -x -3 < 14+x
x-x is 0, so we get
-3 < 14+x
now add -14 to both sides
-3-14 < 14+x-14 which simplifies to -17 < x

the answer is
-17 < x and x < 11
you can write this as
-17 < x < 11

Answer 2

thank you very much

Answer 3

Here is a video if you want to see these worked out
http://www.khanacademy.org/math/algebra/linear_inequalities/compound_absolute_value_inequali/v/absolute-value-inequalities