How do you solve #abs(1/2x-1)<=3#?

1 Answer
Jim G.
Mar 17, 2017

#-4<=x<=8#

Explanation:

The solution to # |x|<=a# is #-a<=x<=a#

We can apply this to the question here.

#-3<=1/2x-1<=3#

To solve, isolate x in the central interval while leaving numeric values in the end intervals.

add 1 to ALL 3 intervals.

#-3+1<=1/2xcancel(-1)cancel(+1)<=3+1#

#rArr-2<=1/2x<=4#

multiply ALL 3 intervals by 2

#rArr-4<=x<=8" is the solution"#

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