How do you solve the absolute value equation #x+absx=28#?

2 Answers
Apr 1, 2015

If #x<0#, the #abs(x)=-x# and #x+absx = 0 !=28# so we must have #x>0# and #absx = x# so we need #x+x=28# and #x=14#

Apr 1, 2015

Answer is #x = 14#

To solve this equation you need to understand what #|x|#
means.
The Magnitude of #x# (denoted #|x|)# simply means the positive side of a number(#x#)

If #x# is positive or #0# (#x>=0#) then #|x| = x#
and if #x# is negative (#x<0#) it imples #|x| = -x#

Example:
#|5| = 5# because #5# is already positive
#|-11| = -(-11)# because #-11# is negative

Back to our question:
# x + |x| = 28#

There will be at most two values of #x#, because there are two possibilities; either #x >=0# or #x<0#

Case 1: # x>=0#
#=> x + x = 28#

#=> 2x = 28 => x = 14#

Case 2: # x<0#
#=> x - x = 28 => 0 = 28#
but we know that # 0!= 28# So the above(last) statement is inconclusive

So the only value we can retain is #x = 14#