How do you solve and write the following in interval notation: #3 < |x| – 5#?

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Answer 1 · 2016-08-02T17:12:01

#-8 > x > 8#

Add 5 to both sides

#8<|x|#

Write as #8<|+-x|#

'.................................................................................
#color(blue)("Consider the case "8<|+x|)#

#" "# This is the same as #color(magenta)(8 < x)#

'.................................................................................
#color(blue)("Consider the case "8<|-x|)#

#" "# This is the same as #color(green)( x < -8)#

Example: suppose #x=-9# then #-9 < -8# is true

Also

#|-9| = +9" " ->" " 8<|x|" " ->" " 8<|-9|" " ->" " 8< 9#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#

#color(blue)(color(magenta)(8 <) x color(green)(< -8)#

Which is the same as: #-8 > x > 8#

Tony B

The open dots mean that x does not assume those values

So we have combined: #x<-8" and "x>8#