How do you solve # |x-4| <1 #? Algebra Linear Inequalities and Absolute Value Absolute Value Inequalities 1 Answer Shwetank Mauria Jul 31, 2016 Solution is #3< x< 5# Explanation: #|x-4|<1# means either #x-4<1# i.e. #x<5# or #-(x-4)<1# or #(-x+4)<1# or #(4-1)< x# i.e. #x>3# Hence solution is #3< x< 5# 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 1149 views around the world You can reuse this answer Creative Commons License