How do you solve #|- x + 1| = 5#?

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Answer 1 · 2017-07-19T08:58:58

#x=6 and -4#

This absolute value condition is basically stating that:

#|+-5|=+5#

The content of the special brackets ( two vertical lines -> absolute value ) is such that we have two condition.

Condition 1: #-x+1=-5#

Condition 2: #-x+1=+5#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider the case "-x+1=-5)#

Multiply everything by (-1) to make #x# positive

#x-1=+5#

Add 1 to both sides

#x+0=5+1=6#

#color(green)( x=6)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider the case "-x+1=+5)#

Multiply everything by (-1)

#x-1=-5#

Add 1 to both sides

#color(green)(x=-4)#