Final answer:
To solve the inequality ||3x −1|+5| <1, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative. The solution to the inequality is x < -1 or x < 7/3.
Step-by-step explanation:
To solve the inequality ||3x −1|+5| <1, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: 3x-1 is positive: In this case, the inequality simplifies to (3x-1) + 5 < 1. Solving this equation, we get x < -1.
Case 2: 3x-1 is negative: In this case, the inequality simplifies to -(3x-1) + 5 < 1. Solving this equation, we get x < 7/3.
Therefore, the solution to the inequality is x < -1 or x < 7/3.