JEE Main Maths: Basic Algebra / Modulus equations questions with solutions

Q1. Solve for x: |2x - 3| = |3x + 5|.

1. x = -8 or x = -2/5
2. x = 8 or x = 2/5
3. x = -8 only
4. x = -2/5 only

Answer: x = -8 or x = -2/5

From |2x - 3| = |3x + 5|, either 2x - 3 = 3x + 5 or 2x - 3 = -(3x + 5). Case 1: 2x - 3 = 3x + 5 -> -x = 8 -> x = -8. Case 2: 2x - 3 = -3x - 5 -> 5x = -2 -> x = -2/5. Both satisfy the original equation, so x = -8 or x = -2/5.