How do you solve and write the following in interval notation: #|2x+3| <= 7#?
1 Answer
Jun 19, 2018
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"#
