Basics & LogarithmsmediumFree

Basics & Logarithms: Find Number Solutions

JEE Maths question with a full step-by-step solution.

Question
Find the number of solutions of ∣x−4∣+3∣x+6∣−2x=5|x-4| + 3|x+6| - 2x = 5 is
Solution
Answer: 0
Critical points: x=−6x = -6 and x=4x = 4. Case 1: x<−6x < -6: (4−x)+3(−x−6)−2x=5  ⟹  −6x−14=5  ⟹  x=−196≈−3.2(4-x) + 3(-x-6) - 2x = 5 \implies -6x - 14 = 5 \implies x = -\dfrac{19}{6} \approx -3.2 Not in x<−6x < -6. Rejected. Case 2: −6≤x≤4-6 \leq x \leq 4: (4−x)+3(x+6)−2x=5  ⟹  22=5(4-x) + 3(x+6) - 2x = 5 \implies 22 = 5 Contradiction. No solution in this interval. Case 3: x>4x > 4: (x−4)+3(x+6)−2x=5  ⟹  2x+14=5  ⟹  x=−92(x-4) + 3(x+6) - 2x = 5 \implies 2x + 14 = 5 \implies x = -\dfrac{9}{2} Not in x>4x > 4. Rejected. Answer: 0
Still stuck on this question?Ask your doubt on WhatsApp
Similar questions
Basics & Logarithms · easy
If x=∏n=12026nx = \prod_{n=1}^{2026} n, then the value of the expression 11log⁡2x+1log⁡3x+⋯+1log⁡2026x\frac{1}{\dfrac{1}{\log_2 x} + \dfrac{1}{\log_3 x} + \cdots + \dfrac{1}{\log_{2026} x}} is
Basics & Logarithms · easy
Number of integral values of xx satisfying the inequality (34)6x+10−x2<2764\left(\dfrac{3}{4}\right)^{6x+10-x^2} < \dfrac{27}{64} is:
Basics & Logarithms · easy
Number of natural numbers for which the number log⁡4−x(x2−14x+45)\log_{4-x}(x^2-14x+45) is defined is:
Basics & Logarithms · easy
The product of all solutions of the equation e5(log⁡ex)2+3=x8e^{5(\log_{e}x)^{2}+3}=x^{8}, x>0x>0, is

Solve more, learn faster

Sign up free to solve more JEE Maths questions and explore doMath — timed drills, mastery sprints, bookmarks, and chapter-wise progress tracking.

Sign up freeExplore doMath