How do you solve and write the following in interval notation: #|2x+3| <= 7#?

1 Answer
Jun 19, 2018

Answer:

#[-5,2]#

Explanation:

#"inequalities of the type "|x|<= a#

#"always have solutions of the form"#

#-a<= x <=a, "hence"#

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

#"isolate "2x" in the middle interval by subtracting 3 from"#
#"all 3 intervals"#

#-7color(red)(-3)<=2x+3color(red)(-3)<=7color(red)(-3)#

#-10<=2x<=4#

#"divide all 3 intervals by 2"#

#-5<= x <=2" is the solution"#

#x in[-5,2]larrcolor(blue)"in interval notation"#