JEE Advanced Maths: Algebra / Modulus questions with solutions

Q1. Find all real x satisfying |x| + |x + 1| + |x + 2| = 3.

1. x = 0 and x = -2
2. x = -1 only
3. x = 0 only
4. no real solution

Answer: x = 0 and x = -2

The piecewise-linear sum has its minimum value 2 at x = -1 and increases on either side; setting it to 3 gives the two boundary solutions.