SOLUTION: |1/2j+4|<7 please help me solve this one step by step. Thanks

Question 767188: |1/2j+4|<7 please help me solve this one step by step. Thanks
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
I assume j is any real number. The reason I say this is that in electrical engineering we use j to represent the imaginary number i, because we use i to represent electrical current. Just a little hint for your work in college.
Now let me give you a real useful bit of knowledge regarding absolute value (also called absolute magnitude when you get into complex variables.) Use the following substitution for |x| when , let
(1) |x| = x and when , let
(2) |x| = -x
In your problem we have
(3) x = j/2 + 4, then we let
(4) |j/2 + 4| = j/2 + 4 when
(5) or
(6) or
(7)
Now apply this to the given inequality
(8) |j/2 + 4| < 7 and get
(9) ; or
(10) j/2 < 7 - 4 or
(11) j < 2*3 or
(12) j < 6
Now couple (12) with the condition of (9) and get
(13)
Now we need to determine the limits on j when j/2 + 4 is negative as in (2).
Then we have
(14) -x = -j/2 - 4, then we let
(15) |j/2 + 4| = -j/2 - 4 when
(16) or
(17) or
(18)
Now apply this to the given inequality
(19) |j/2 + 4| < 7 and get
(20) ; or
(21) -j/2 < 7 + 4 or
(22) j > -22 Note: we reversed the inequality because we multiplied both sides by a negative number (-2).
Now couple (22) with the condition of (20) and get
(23)
By combining (13) and (23) we get the final limits on j as
(24) and
Since upper limit (-8) of the first inequality is equal to the lower limit (-8) of the second inequality, we can write the overall inequality as
(25)
Answer:

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