You can
put this solution on YOUR website! |z - 1| < 4
Rule for rwmoving absolute values:
1. |Ax + B| < C where C is a positive number
can be rewritten as this:
" -C < Ax + B < C "
2. |Ax + B| > C where C is a positive number
can be rewritten as this
" -C < Ax + B OR Ax + B > C "
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|z - 1| < 4
This is case 1, so we rewrite it as
-4 < z - 1 < 4
Add 1 to all three sides
-4 + 1 < z - 1 + 1 < 4 + 1
-3 < z < 5
which in set-builder notation is {z|-3 < z < 5}
and in interval notation is (-3, 5)
Edwin
AnlytcPhil@aol.com
