How do you solve the equation #absx=x+3#?

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Answer 1 · 2017-05-09T19:12:55

Use the definition:

#|x|= {(x;x >=0),(-x;x < 0):}#

Given: #absx=x+3#

Use the definition to break into two equations:

#x = x+3; x >=0# and #-x = x+3; x < 0#

Subtract x from both sides of both equations:

#0 = 3; x >=0# and #-2x = 3; x < 0#

Discard the first equation, because it can never be true:

#-2x = 3; x < 0#

Divide both sides by -2 and drop the restriction because it will obviously be true:

#x = -3/2#

Check:

#|-3/2| = -3/2+3#

#3/2=3/2#

This checks

#x = -3/2 larr# answer.