Exams › JEE Advanced › Maths

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

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

Solution

|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.

Related JEE Advanced Maths questions

• Solve the equation |2x - 5| = 7 for x.
• In a chemistry class, there are 20 students, while a physics class has 30 students. If 10 students are enrolled in both classes, and the two classes are held at separate times, determine the value of k/8, where k represents the total number of students attending either class.
• Given that A represents the divisors of 15, B contains prime numbers less than 10, and C includes even numbers less than 9, how many elements are there in the intersection of (A ∪ C) and B?
• Identify the periodic function among the following:
• The function f(x) = √|x² - 5| x + 6 + √8 + 2|x| - |x|² is defined as a real number for values of x within which range?
• Let f(x) = 4x / (4x² + 2). If the sum of the integrals ∫(1/1997) + ∫(2/1997) +... + ∫(1196/1997) equals 499q, what is the value of q?

⚔️ Practice JEE Advanced Maths free + battle 1v1 →