How do you solve #abs(2x + 2) - 7 <= -5#?

1 Answer
Jun 14, 2015

Answer:

#-2 <= x <= 0#

Explanation:

#abs(2x+2) -7 <= -5#
#color(white)("XXXX")##rArr abs(2x+2) <= 2#

If #(2x+2) < 0##color(white)("XXXX")##rarr x<-1#
#abs(2x+2) <=2#
means #(-2x-2) <=2#
#color(white)("XXXX")##-2x <=4#
#color(white)("XXXX")##x>= -2#

If #(2x+2) >=0##color(white)("XXXX")##rarr x>=-1#
#abs(2x+2) <= 2#
means #(2x+2) <=2#
#color(white)("XXXX")##x<=0#

for #x<-1#, #rarr x>=-2#
for #x>=-1#, #rarr x<=0#

So #-2<=x<=0#