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How many integers x satisfy 2x + 3  < 6 ?
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16 Jul 2018, 19:54
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Re: How many integers x satisfy 2x + 3  < 6 ?
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16 Jul 2018, 21:57
Bunuel wrote: How many integers x satisfy 2x + 3  < 6 ?
A. 1
B. 2
C. 6
D. 7
E. 8 two cases 1) 2x+3 >0 so \(2x+3<6..............2x<3.............x<\frac{3}{2}\) 2) 2x+3<0 so \(2x+3>6..............2x>9.............x>\frac{9}{2}\) integers value 4, 3, 2, 1, 0, 1  6 values C
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Re: How many integers x satisfy 2x + 3  < 6 ?
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16 Jul 2018, 22:16
Bunuel wrote: How many integers x satisfy 2x + 3  < 6 ?
A. 1
B. 2
C. 6
D. 7
E. 8 Given, \(2x + 3  < 6\) Or, \(x(\frac{3}{2})< 3\) (Dividing both sides of the inequality by 2) Or, \((\frac{3}{2}3) < x < (\frac{3}{2}+3)\) Or, \(4.5<x<1.5\) So, Possible integer values of x: 4, 3, 2, 1, 0, 1 So, no of integers are 6. Ans. (C)
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Re: How many integers x satisfy 2x + 3  < 6 ?
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16 Jul 2018, 22:32
+1 for C. 2x+3<6 Possible cases :Case 1 = (2x + 3) <6 = 2x  3 <6 = 2x < 9 = x > 9/2 = x > 4.5 Case 2 > 2x + 3 <6 = 2x < 3 = x < 3 / 2 = x < 1.5 Combining : 4.5 < x < 1.5 Therefore, x = 4, 3, 2, 1, 0, 1 Number of integers = 6. Hence, C.
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How many integers x satisfy 2x + 3  < 6 ?
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17 Jul 2018, 03:55
Bunuel wrote: How many integers x satisfy 2x + 3  < 6 ?
A. 1
B. 2
C. 6
D. 7
E. 8 As this problem is on absolute value , we must have a certain range of values. Case 1 : 2x + 3 = positive. 2x + 3 < 6 x < 1.5 case 2: 2x +3 = negative 2x  3 <6 2x < 9 x < 4.5. So, 4.5 < x < 1.5 Integers fall into the range : 1, 0 , 1, 2 , 3 , 4 There are 6 values in total. The best answer is C.



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Re: How many integers x satisfy 2x + 3  < 6 ?
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19 Jul 2018, 05:49
Bunuel wrote: How many integers x satisfy 2x + 3  < 6 ?
A. 1
B. 2
C. 6
D. 7
E. 8 \(2x + 3  < 6\) \(6 < 2x + 3 < 6\) \(3 < 2x < 9\) \(1.5 < x < 4.5\) Therefore, 1, 0, 1, 2, 3, 4 are the required values. So C
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Re: How many integers x satisfy 2x + 3  < 6 ?
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19 Jul 2018, 16:19
Bunuel wrote: How many integers x satisfy 2x + 3  < 6 ?
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
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