|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  "

====================================================

|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