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For all integral values of x,
|x - 4| x< 5
- a)-1 ≤x≤5
- b)1 ≤x≤5
- c)-1 ≤ x ≤ 1
- d)x<5
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
For all integral values of x,|x- 4| x< 5a)-1 ≤x≤5 b)1 ≤x&l...
At x = 0 inequality is satisfied, option (b) is rejected.
At x = 2, inequality is satisfied, option (c) is rejected.
At x = 5, LHS = RHS.
Thus, option (d) is correct.
Most Upvoted Answer
For all integral values of x,|x- 4| x< 5a)-1 ≤x≤5 b)1 ≤x&l...
If x is greater than or equal to 4, then |x-4| = x-4 and the expression becomes (x-4)x = x^2 - 4x.
If x is less than 4, then |x-4| = -(x-4) = 4-x and the expression becomes (4-x)x = 4x - x^2.
So the overall expression is:
x^2 - 4x if x >= 4
4x - x^2 if x < />
We can graph these two equations separately and then combine them into one graph:
When x is greater than or equal to 4, the graph is a parabola opening upwards, with its vertex at (2, -4).
When x is less than 4, the graph is a parabola opening downwards, with its vertex at (2, 4).
We can see that the two parabolas intersect at x=2, where the value of the expression is -4.
Therefore, the values of the expression for all integral values of x are:
-20, -12, -6, -4, -4, -6, -12, -20... (with x=2 being the minimum value).
If x is less than 4, then |x-4| = -(x-4) = 4-x and the expression becomes (4-x)x = 4x - x^2.
So the overall expression is:
x^2 - 4x if x >= 4
4x - x^2 if x < />
We can graph these two equations separately and then combine them into one graph:
When x is greater than or equal to 4, the graph is a parabola opening upwards, with its vertex at (2, -4).
When x is less than 4, the graph is a parabola opening downwards, with its vertex at (2, 4).
We can see that the two parabolas intersect at x=2, where the value of the expression is -4.
Therefore, the values of the expression for all integral values of x are:
-20, -12, -6, -4, -4, -6, -12, -20... (with x=2 being the minimum value).
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Community Answer
For all integral values of x,|x- 4| x< 5a)-1 ≤x≤5 b)1 ≤x&l...
At x = 0 inequality is satisfied, option (b) is rejected.
At x = 2, inequality is satisfied, option (c) is rejected.
At x = 5, LHS = RHS.
Thus, option (d) is correct.
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For all integral values of x,|x- 4| x< 5a)-1 ≤x≤5 b)1 ≤x≤5c)-1 ≤ x ≤1 d)x<5Correct answer is option 'D'. Can you explain this answer?
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For all integral values of x,|x- 4| x< 5a)-1 ≤x≤5 b)1 ≤x≤5c)-1 ≤ x ≤1 d)x<5Correct answer is option 'D'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about For all integral values of x,|x- 4| x< 5a)-1 ≤x≤5 b)1 ≤x≤5c)-1 ≤ x ≤1 d)x<5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For all integral values of x,|x- 4| x< 5a)-1 ≤x≤5 b)1 ≤x≤5c)-1 ≤ x ≤1 d)x<5Correct answer is option 'D'. Can you explain this answer?.
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