Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Basics of Mathematics

NDA 2023 · Mathematics · Basics of Mathematics

How many real numbers satisfy the equation |x-4|+|x-7|=15 ?

How many real numbers satisfy the equation ∣x−4∣+∣x−7∣=15?|x-4|+|x-7|=15 ?

Options

  1. AOnly one
  2. BOnly two
  3. COnly three
  4. DInfinitely many

Correct answer

B. Only two

Step-by-step solution

∣x−4∣+∣x−7∣=15|x-4|+|x-7|=15 Case 1: x<44−x+7−x=1511−2x=152x=−4x=−2⇒\quad x < 44-x+7-x=1511-2 x=152 x=-4x=-2 \Rightarrow One solution. Case 2: 4≤x<7x−4+7−x=15\quad 4 \leq x < 7x-4+7-x=15 No solution Case 3: x≥7x−4+x−7=152x=26x=13⇒\quad x \geq 7x-4+x-7=152 x=26x=13 \Rightarrow One solution ∴\therefore \quad Total 2 solutions; x=−2,13x=-2,13.
Practice Basics of Mathematics on Quantrex Academy →

More from Basics of Mathematics

All Basics of Mathematics questions Full Basics of Mathematics list Basics of Mathematics JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs