How do you solve #|-2(x+2)|=1#?

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Answer 1 · 2016-09-08T10:07:42

#x= -5/2" or "x=-3/2#

Consider #|-2(x+2)|=1# as:

#|-2(x+2)|=|+-1|#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider the case "-2(x+2)=+1"#

This means that #x+2= -1/2 => x=-5/2#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider the case "-2(x+2)=-1)#

This means that #x+2=+1/2 => x= -3/2#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Check: consider the left hand side")#

#|-2(-5/2+2)| = |-2(-1/2)| = |+1|=1 color(red)(" Works")#

#|-2(-3/2+2)|= |-2(+1/2)| = |-1| = 1 color(red)(" Works")#