What is the solution set for #abs(3x – 2) < 7#?
1 Answer
Aug 22, 2015
Explanation:
Since you're dealing with the absolute value of a variable expression, you must take into account the fact that this expression can be negative or positive.
#3x-2>0 implies |3x-2| = 3x-2#
The inequality becomes
#3x-2 < 7#
#3x < 9 implies x < 3#
#(3x-2)<0 implies |3x-2| = -(3x-2)#
This time, you get that
#-(3x-2) < 7#
#-3x + 2 < 7#
#-3x < 5 implies x > -5/3#
This means that your original inequality will be true for any value of
The solution interval will thus be