JEE Main Maths: Basic Mathematics / Modulus questions with solutions

Q1. Solve the equation |x| - x = 0 for real x.

1. x >= 0 (all non-negative reals)
2. x <= 0 (all non-positive reals)
3. x = 0 only
4. all real x

Answer: x >= 0 (all non-negative reals)

|x| - x = 0 means |x| = x. By definition |x| = x exactly when x is non-negative; for x < 0, |x| = -x != x. Therefore the solution set is all x >= 0.

Q2. Solve the equation |2x - 5| = 7 for x.

1. x = 6 or x = -1
2. x = 6 or x = 1
3. x = -6 or x = 1
4. x = 6 only

Answer: x = 6 or x = -1

Remove the modulus by considering both sign cases of (2x - 5), then solve each linear equation.