How do you solve #abs(3x+2)<7#?

1 Answer
Apr 16, 2017

Answer:

#-3 < x<5/3#

Explanation:

Inequalities of the type #|x|< a# always have solutions of the form

#-a < x< a#

#rArr-7 < 3x+2 < 7#

#color(blue)" Isolate " x " in the centre interval"#

#"subtract 2 from ALL three intervals"#

#-7-2 < 3xcancel(+2)cancel(-2)<7-2#

#rArr-9 < 3x < 5#

#"divide ALL three intervals by 3"#

#(-9)/3 < (cancel(3) x)/cancel(3) < 5/3#

#rArr-3 < x < 5/3" is the solution"#