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

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) (Show Source): You can put this solution on YOUR website!

I know the left side cannot be negative,
since it's an absolute value, so both
these must be true:

-----------------------
Suppose , then

-----------------------
Suppose ,
(1)
and
(2)
------------------
(1)
(1)
(1)
------------------
(2)
(2)
(2)
------------------
I have 3 equations now:

all of which must be true
includes all three, so
that is my answer

RELATED QUESTIONS
What would be the solution for x in the rational equation: x^2/(x-3) = (x+2)/(2x-5) (answered by josgarithmetic)

5x+8=3x-4= I think I got the right answer on the test. I wrote 6 as the answer but I... (answered by jim_thompson5910)

Let g(x)=9x²-2. Find the average rate of change of the function as x changes from -8 to... (answered by ikleyn,math_tutor2020)

Please respond by 9:00 am tomorrow because I must know before my finals, and let me thank (answered by ikleyn,jim_thompson5910,josgarithmetic)

solve -3x/x+4=6/x-11 the answer is 3 but I don't know how to solve... (answered by stanbon)

Simplify |-3+4 x-2| the answer key says 11 but i don't know how that's the... (answered by Solver92311,ikleyn)

I am having the hardest time with this one. When I try to plug in x it does not work for (answered by rapaljer)

Solve |x+4|<7 the answer is -11 (answered by josgarithmetic)
Hello there. I need help on a problem. It says Use elimination to solve each system of... (answered by jim_thompson5910,solver91311)