Question 1139418: |2(|x-3|)-7| <5
How would you solve without square root method?
Answer by ikleyn(52790)   (Show Source):
You can put this solution on YOUR website! .
| 2*(|x-3|)-7 | < 5
is equivalent to
-5 < 2*|x-3| - 7 < 5
is equivalent (after adding 7 to each of 3 parts of the inequality)
-5 + 7 < 2*|x-3| < 5 + 7
is the same as
2 < 2*|x-3| < 12
is equivalent to (after dividing all the three terms of the inequality by 2)
1 < |x-3| < 6.
The solutions to the last inequality are those values of x (those numbers or points in the number line)
that are remoted from the point x= 3 farther than 1 unit and closer than 6 units.
Obviously, these points (numbers, solutions) are
-3 < x < 2 and/or 4 < x < 9.
ANSWER. The solution set to the original inequality is the union of two intervals {-3,2) and (4,9): (-3,2) U (4,9).
Solved, answered, explained and completed.
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