Expert: Sherry Wallin - 5/12/2010

Question
ex.modulus of 3x+4=1.
we write as
-(3x+4)=1,and
(3x+4)=1.but modulus of any value is always positive.
so why do we write -(3x+4)=1.

Answer
Andrew~
    You are assuming that -(3x+4) is negative because of the minus sign, but what if x is a number like (-5/3) that makes it true?
    It would help if you referred to these problems as absolute value since that is more common. Actually think of it this way:

|3x+4| = +-1 -> 3X+4 = 1 OR 3x+4 = -1 and solve each for x. The 'modulus' isn't negative, just the value of x that would make the statement true.

Note: |3x+4| = +-1 is the same as saying 3x+4 = 1 or -(3x+4) = 1.

And finally, I noticed you used the word 'and' and it is 'or'. Notice when you solve for x in each case you get x = -5/3, x = -1 so x will never be the same in each case so it can't be and.

Math Prof