How do you solve and graph #abs(x-4)<9#?

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Answer 1 · 2018-03-18T09:19:08

The solution is #x in (5, 13)#

There are #2# solutions for Inequalities with absolute values

#|x-4|<9#

#x-4<9# and #-x+4<9#

Therefore,

#x<13# and #x>5#

The solutions are

#S_1= x in (-oo,13)#

and #S_2= x in (5,+oo) #

The solution

#S= S_1 nn S_2#

#S=x in (5, 13)#

See the graph below

graph{|x-4|-9 [-18.02, 18.03, -9.01, 9.01]}