How do you solve #1/2abs(2x + 1 )> 2 #? Algebra Linear Inequalities and Absolute Value Absolute Value Inequalities 1 Answer Ahmemaru · Stefan V. Mar 11, 2018 #x > 3/2 or x < -5/2# in interval notation #(-oo, -5/3) uu (3/2, oo)# Explanation: #1/2|2x+1|>2# #|2x+1|>4# #2x+1>4# or #2x+1<-4# so #-4>2x+1>4# #-5>2x>3# #-5/2>x>3/2# #x > 3/2 or x < -5/2# #(-oo, -5/3)uu(3/2, oo)# Answer link Related questions How do you solve absolute value inequalities? When is a solution "all real numbers" when solving absolute value inequalities? How do you solve #|a+1|\le 4#? How do you solve #|-6t+3|+9 \ge 18#? How do you graph #|7x| \ge 21#? Are all absolute value inequalities going to turn into compound inequalities? How do you solve for x given #|\frac{2x}{7}+9 | > frac{5}{7}#? How do you solve #abs(2x-3)<=4#? How do you solve #abs(2-x)>abs(x+1)#? How do you solve this absolute-value inequality #6abs(2x + 5 )> 66#? See all questions in Absolute Value Inequalities Impact of this question 1629 views around the world You can reuse this answer Creative Commons License