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How many integers x satisfy
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16 Jul 2018, 00:00
16 Jul 2018, 00:00
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72% (01:14) correct
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How many integers \(x\) satisfy \(|2x + 3 | < 6\)
A. 1
B. 2
C. 6
D. 7
E. 8
A. 1
B. 2
C. 6
D. 7
E. 8
Re: How many integers x satisfy
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17 Jul 2018, 07:41
17 Jul 2018, 07:41
1
Carcass wrote:
How many integers \(x\) satisfy \(|2x + 3 | < 6\)
A. 1
B. 2
C. 6
D. 7
E. 8
A. 1
B. 2
C. 6
D. 7
E. 8
As we are dealing with modulus we have to consider both negative and positive aspects.
Case 1 : when 2x + 3 is positive.
2x + 3 < 6
x < 1.5.
Case 2: when 2x + 3 is negative .
-2x -3 < 6
x > -4.5.
So,
-4.5 <x<1.5.
There are 6 values in total : -4, -3 , -2, -1, 0 , 1.
The best answer is C.
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Re: How many integers x satisfy
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19 Jul 2018, 15:59
19 Jul 2018, 15:59
1
Expert Reply
Carcass wrote:
How many integers \(x\) satisfy \(|2x + 3 | < 6\)
A. 1
B. 2
C. 6
D. 7
E. 8
A. 1
B. 2
C. 6
D. 7
E. 8
Recall that if k is a positive constant and |ax + b| < k, then -k < ax + b < k. So we can solve the given inequality by removing the absolute value sign and change it to the following double inequality:
-6 < 2x + 3 < 6
-9 < 2x < 3
-9/2 < x < 3/2
-4.5 < x < 1.5
The integers x can be are: -4, -3, -2, -1, 0, and 1. So there are 6 integers that satisfy the inequality.
Answer: C
