How do you solve #abs(2x-9)<=11#?

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Answer 1 · 2018-04-17T00:51:25

#x<= 10 and x>=-1#

#|2x - 9| <= 11#

We need to start by solving the absolute value

We know either #2x - 9 <=11 and 2x - 9 >=-11#

Now we can solve the first one:

#2x - 9 <= 11#

Add #9# on both sides

#2x - 9 + 9 <= 11 + 9#

#2x <= 20#

Divide both sides by #2#

#(cancel2x)/cancel2 <= 20/2#

#x<=10#

Now we can solve the second one

#2x - 9 >= -11#

Add #9# on both sides

#2x - 9 + 9 >= -11 + 9#

#2x >= -2#

Then divide both sides by #2#

#(2x)/2 >= (-2)/2#

#x >=-1#

Thus,

The answers are:

#x <=10 and x>=-1#