SOLUTION: Solve: | | 3x+7| | <6 The answer I got were x<4,x>14 but I don't know how I to write it. Please let me know if my answer iscorrect

Algebra ->  Absolute-value -> SOLUTION: Solve: | | 3x+7| | <6 The answer I got were x<4,x>14 but I don't know how I to write it. Please let me know if my answer iscorrect      Log On


   



Question 988988: Solve: | | 3x+7| | <6
The answer I got were x<4,x>14 but I don't know how I to write it. Please let me know if my answer iscorrect

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+abs%28+3x+%2B+7+%29+%3C+6+
I know the left side cannot be negative,
since it's an absolute value, so both
these must be true:
+abs%28+3x+%2B+7+%29+%3E=+0+
+abs%28+3x+%2B+7+%29+%3C+6+
-----------------------
Suppose +abs%28+3x+%2B+7+%29+=+0+, then
+x+=+-7%2F3+
-----------------------
Suppose +abs%28+3x+%2B+7+%29+%3C6+,
(1) +3x+%2B+7+%3C+-6+
and
(2) +3x+%2B+7+%3C+6+
------------------
(1) +3x+%3C+-6+-+7+
(1) +3x+%3C+-13+
(1) +x+%3C+-13%2F3+
------------------
(2) +3x+%3C+6+-7+
(2) +3x+%3C+-1+
(2) +x+%3C+-1%2F3+
------------------
I have 3 equations now:
+x+=+-7%2F3+
+x+%3C+-13%2F3+
+x+%3C+-1%2F3+
all of which must be true
+x+%3C+-1%2F3+ includes all three, so
that is my answer