Hi, there-- THE PROBLEM: Solve the following inequality. Enter the answer in interval notation |3-4x|<7 A SOLUTION: The absolute value inequality has two branches. Either the expression inside the absolute value signs (3-4x) can be positive or it can be negative. In either case, the absolute value returns a positive value. We deal with each case separately. CASE I :: Suppose 3-4x is positive. Then 3 - 4x < 7 To simplify, we subtract 3 from both sides of the inequality. -4x < 7-3 -4x < 4 To isolate x on the left, we divide both sides of the inequality by -4. Whenever we divide the terms of an inequality by a negative number, we must reverse the direction of the inequality. x > -1 CASE II :: Suppose that 3 - 4x is negative. Then -(3 - 4x) < 7 Use the distributive property to clear the parentheses. -3 + 4x < 7 To simplify, add 3 to both sides of the inequality. 4x < 7 + 3 4x < 10 Divide both sides of the equation by 4. x < 10/4 x < 2.5 Combine the two cases, we have x > -1 OR x < 2.5 The numbers that satisfy this inequality are between -1 and 2.5. In interval notation, we write (-1, 2.5). Hope this helps! Feel free to email if you have any questions about the solution. Good luck with your math, Mrs. F math.in.the.vortex@gmail.com