How do you solve #abs(x-1)<=9#? Algebra Linear Inequalities and Absolute Value Absolute Value Inequalities 1 Answer Shwetank Mauria Sep 9, 2016 Solution is #-8<=x<=10# Explanation: #|x-1|<=9# means either #x-1<=9# or #-(x-1)<=9# #x-1<=9# #hArrx<=9+1# or #x<=10# #-(x-1)<=9# #hArr-x+1<=9# or #1-9<=x# or #-8<=x# Hence, solution is #-8<=x<=10# 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 1207 views around the world You can reuse this answer Creative Commons License