JEE Main Maths: Basic Maths / Modulus questions with solutions

Q1. Solve the equation |2x + 5| = 2 for x.

1. x = -3/2 or x = -7/2
2. x = 3/2 or x = 7/2
3. x = -3/2 only
4. x = -7/2 only

Answer: x = -3/2 or x = -7/2

|2x + 5| = 2 means 2x + 5 = 2 or 2x + 5 = -2. First: 2x = -3, x = -3/2. Second: 2x = -7, x = -7/2.

Q2. Solve for real x: |x - 3| = -1.

1. No solution (empty set)
2. x = 2
3. x = 4
4. x = 2 or x = 4

Answer: No solution (empty set)

Absolute value is always non-negative: |x - 3| >= 0. The right side is -1 < 0, so the equation has no real solution; the solution set is empty.