How do you solve and graph #abs(2z-9)<=1#?

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Answer 1 · 2017-09-20T19:08:03

Find the two values of #z# where the equation #|2z-9| = 1# is true.
The inequality will be true for those values and all values in between.

Solve: #|2z-9| = 1#

Separate into two equations:

#2z-9 = 1# and #-(2z-9) = 1#

Multiply both sides of the second equation by -1:

#2z-9 = 1# and #2z-9 = -1#

Add 9 to both sides of both equations:

#2z = 10# and #2z = 8#

Divide both sides of both equations by 2:

#z = 5# and #z = 4#

The inequality will be true between these values:

#4 <= z <= 5#

Answer 2 · 2017-09-20T19:09:41

z=4, z=5

#|2z-9|<=1# gives two equations
1. #(2z-9)<=1#
#=>2z<=10#
#=>z<=5#
2. #-(2z-9)<=1#
#=>-2z+9<=1#
#=>-2z<=-8#
#=>2z>=8#
#=>z>=4#

So Values of z
#z=4, z=5#

in Graph there are two lines z=4 and z=5