How do you solve abs(4x-3)<7? Algebra Linear Inequalities and Absolute Value Absolute Value Inequalities 1 Answer Shwetank Mauria Jul 28, 2016 -1 < x < 2.5 - i.e. x is between -1 and 2.5 Explanation: As |4x-3|<7, either 4x-3<7 i.e, 4x<7+3 or 4x=10 i.e. x<10/4 i.e. x<2.5 or -(4x-3)<7 i.e. -4x+3<7 or 3-7<4x or 4x>-4 i.e. x>-1 Hence, we have x<2.5 and x>-1, which can be written better as -1 < x < 2.5 - i.e. x is between -1 and 2.5 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 1686 views around the world You can reuse this answer Creative Commons License