Basics & LogarithmsmediumFree

Basics & Logarithms: Find Number Single Digit Negative Integers Satisfying

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

Question
Find the number of single digit negative integers satisfying ∣∣x−6∣−∣x+6∣∣=12\big||x-6| - |x+6|\big| = 12 is
Solution
Answer: 4
Step 1: Write a=x−6a = x-6 and b=x+6b = x+6. Note a−b=−12a - b = -12, so ∣a−b∣=12|a-b| = 12. Step 2: The reverse triangle inequality gives ∣∣a∣−∣b∣∣≤∣a−b∣=12\big||a|-|b|\big| \leq |a-b| = 12. Equality ∣∣a∣−∣b∣∣=∣a−b∣\big||a|-|b|\big| = |a-b| holds if and only if ab≥0ab \geq 0. Step 3: (x−6)(x+6)≥0  ⟹  x2≥36  ⟹  ∣x∣≥6(x-6)(x+6) \geq 0 \implies x^2 \geq 36 \implies |x| \geq 6, i.e., x≤−6x \leq -6 or x≥6x \geq 6. Step 4: Single digit negative integers satisfying x≤−6x \leq -6: {−6,−7,−8,−9}\{-6, -7, -8, -9\}. Count =4= 4. Answer: 4
Still stuck on this question?Ask your doubt on WhatsApp
Similar questions
Basics & Logarithms · easy
The product of all solutions of the equation e^ 5(log(e)x)^(2)+3 =x^(8) , x>0 , is
Basics & Logarithms · easy
The number of real solutions of the equation x (x^(2)+3|x|+5|x-1|+6|x-2| )=0 is
Basics & Logarithms · easy
If a+b+c=1 , ab+bc+ca=2 and abc=3 , then the value of a^(4)+b^(4)+c^(4) is equal to
Basics & Logarithms · easy
Sum of all the values of x satisfying the equation log(17)log(11)(√(x+11)+√(x)) = 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