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Find the number of integral values of x that satisfy
|x2 + 3x - 1| < 2|x| + 5
Correct answer is '7'. Can you explain this answer?
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Verified Answer
Find the number of integral values of x that satisfy|x2 + 3x - 1| <...
|x2 + 3x - 1| < 2|x| + 5
We have to find out the boundary points for each modulus and adjust the + or - sign after removing the modulus.
For the left expression, x2 + 3x - 1y = x, the roots are 
√13 ≈ 3.6
So, the approx roots are -3.3 and +0.3.
√13 ≈ 3.6
So, the approx roots are -3.3 and +0.3.
For the right side of the expression, the boundary point is 0
Let us denote the same in the number line.
For R1,
|x2 + 3x - 1| < 2|x| + 5
x2 + 3x - 1 < 2x + 5
x2+ x - 6 < 0
(x-2) (x +3) < 0
x ∈ (-3,2)
Overlapping region is
Overlapping region is
For R2,
|x2 + 3x - 1| < 2|x| + 5
-x2 - 3x + 1 < 2x + 5
-x2 - 5x - 4 < 0
x2 + 5x + 4 > 0
(x + 1) (x + 4) > 0
x ∈ R −(−4,−1)
Overlapping region is
For R3,
|x2 + 3x - 1| < 2|x| + 5
-x2 - 3x + 1 < - 2x + 5
- x2 - x - 4 < 0
- x2 + x + 4 > 0
This is possible for all values of x. Therefore the overlapping region is
This is possible for all values of x. Therefore the overlapping region is
For R4,
|x2 + 3x - 1| < 2|x| + 5
-x2 - 3x + 1 < - 2x + 5
x2 + 5x - 6 < 0
(x + 6) (x -1) < 0
x ∈ (−6, 1)
Hence, the overall overlapping region is
Integral values are {-5, -4, -3, -2, -1, 0, 1}
Most Upvoted Answer
Find the number of integral values of x that satisfy|x2 + 3x - 1| <...
To find the number of integral values of x that satisfy the given expression, we need to determine when the expression inside the absolute value brackets equals 0.
Setting x^2 + 3x - 1 = 0, we can solve this quadratic equation using factoring or the quadratic formula:
(x + 1)(x - 1) = 0
This equation is satisfied when x = -1 or x = 1.
Therefore, there are 2 integral values of x that satisfy the given expression.
Setting x^2 + 3x - 1 = 0, we can solve this quadratic equation using factoring or the quadratic formula:
(x + 1)(x - 1) = 0
This equation is satisfied when x = -1 or x = 1.
Therefore, there are 2 integral values of x that satisfy the given expression.
Community Answer
Find the number of integral values of x that satisfy|x2 + 3x - 1| <...
|x2 + 3x - 1| < 2|x| + 5
We have to find out the boundary points for each modulus and adjust the + or - sign after removing the modulus.
For the left expression, x2 + 3x - 1y = x, the roots are 
√13 ≈ 3.6
So, the approx roots are -3.3 and +0.3.
√13 ≈ 3.6
So, the approx roots are -3.3 and +0.3.
For the right side of the expression, the boundary point is 0
Let us denote the same in the number line.
For R1,
|x2 + 3x - 1| < 2|x| + 5
x2 + 3x - 1 < 2x + 5
x2+ x - 6 < 0
(x-2) (x +3) < 0
x ∈ (-3,2)
Overlapping region is
Overlapping region is
For R2,
|x2 + 3x - 1| < 2|x| + 5
-x2 - 3x + 1 < 2x + 5
-x2 - 5x - 4 < 0
x2 + 5x + 4 > 0
(x + 1) (x + 4) > 0
x ∈ R −(−4,−1)
Overlapping region is
For R3,
|x2 + 3x - 1| < 2|x| + 5
-x2 - 3x + 1 < - 2x + 5
- x2 - x - 4 < 0
- x2 + x + 4 > 0
This is possible for all values of x. Therefore the overlapping region is
This is possible for all values of x. Therefore the overlapping region is
For R4,
|x2 + 3x - 1| < 2|x| + 5
-x2 - 3x + 1 < - 2x + 5
x2 + 5x - 6 < 0
(x + 6) (x -1) < 0
x ∈ (−6, 1)
Hence, the overall overlapping region is
Integral values are {-5, -4, -3, -2, -1, 0, 1}
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Find the number of integral values of x that satisfy|x2 + 3x - 1| < 2|x| + 5Correct answer is '7'. Can you explain this answer?
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Find the number of integral values of x that satisfy|x2 + 3x - 1| < 2|x| + 5Correct answer is '7'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Find the number of integral values of x that satisfy|x2 + 3x - 1| < 2|x| + 5Correct answer is '7'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the number of integral values of x that satisfy|x2 + 3x - 1| < 2|x| + 5Correct answer is '7'. Can you explain this answer?.
Find the number of integral values of x that satisfy|x2 + 3x - 1| < 2|x| + 5Correct answer is '7'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Find the number of integral values of x that satisfy|x2 + 3x - 1| < 2|x| + 5Correct answer is '7'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the number of integral values of x that satisfy|x2 + 3x - 1| < 2|x| + 5Correct answer is '7'. Can you explain this answer?.
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