How do you solve -4x-1>3 or x+2>7?

1 Answer
Sep 11, 2015

Answer:

#x < -1 or x > 5#
#color(white)("XXX")#OR
#abs(x-2) > 3#

Explanation:

Part 1
#color(white)("XXX")-4x-1 > 3#
add #4x-3# to both sides
#color(white)("XXX")-4 > 4x#
divide by #4#
#color(white)("XXX")-1 > x#
or, equivalently
#color(white)("XXX")x < -1#

Part 2
#color(white)("XXX")x+2 > 7#
subtract #2# from both sides
#color(white)("XXX")x > 5#

Note that for #x < -1# or #x > 5#
#color(white)("XXX")x# must be further that #2# the midpoint between #(-1)# and #(5)# (i.e. from #3#)
So
#color(white)("XXX")abs(x-2) > 3#