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Updated on: 22 Apr 2023, 01:23
Originally posted by heyholetsgo on 18 Aug 2010, 10:06.
Last edited by Bunuel on 22 Apr 2023, 01:23, edited 3 times in total.
Last edited by Bunuel on 22 Apr 2023, 01:23, edited 3 times in total.
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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56% (02:00) correct
44%
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wrong
based on 852
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If 8x > 4 + 6x, what is the value of the integer x?
(1) 6 – 5x > -13
(2) 3 – 2x < -x + 4 < 7.2 – 2x
(1) 6 – 5x > -13
(2) 3 – 2x < -x + 4 < 7.2 – 2x
Could anybody tell me when it is appropriate to add up equations? That's what I did and it didn't work...
18 Aug 2010, 10:18
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If 8x > 4 + 6x, what is the value of the integer x?
First, note that we are given that x is an integer.
Next, simplify the given inequality:
(1) \(6-5x>-13\);
Since x is an integer and \(x > 2\), then \(x = 3\). Sufficient.
(2) \(3-2x<-x+4<7.2-2x\)
Consider only the following part:
Since x is an integer and \(x > 2\), then \(x = 3\). Sufficient.
Answer: D.
There is no need to add inequalities in this case. However, if you are interested:
You can only add inequalities when their signs are in the same direction:
If \(a > b\) and \(c > d\) (signs in the same direction: \( > \) and \( > \)) --> \(a + c > b + d\).
You can only apply subtraction when their signs are in the opposite directions:
If \(a > b\) and \(c < d\) (signs in opposite direction: \( > \) and \( < \)) --> \(a - c > b - d\) (take the sign of the inequality you subtract from).
Hope it helps.
First, note that we are given that x is an integer.
Next, simplify the given inequality:
- \(8x>4+6x\);
\(2x>4\);
\(x>2\).
(1) \(6-5x>-13\);
- \(19>5x\);
\(3.8>x\).
Since x is an integer and \(x > 2\), then \(x = 3\). Sufficient.
(2) \(3-2x<-x+4<7.2-2x\)
Consider only the following part:
- \(-x+4<7.2-2x\);
\(x<3.2\)
Since x is an integer and \(x > 2\), then \(x = 3\). Sufficient.
Answer: D.
heyholetsgo
There is no need to add inequalities in this case. However, if you are interested:
You can only add inequalities when their signs are in the same direction:
If \(a > b\) and \(c > d\) (signs in the same direction: \( > \) and \( > \)) --> \(a + c > b + d\).
- Example: \(3 < 4\) and \(2 < 5\) --> \(3 + 2 < 4 + 5\).
You can only apply subtraction when their signs are in the opposite directions:
If \(a > b\) and \(c < d\) (signs in opposite direction: \( > \) and \( < \)) --> \(a - c > b - d\) (take the sign of the inequality you subtract from).
- Example: \(3 < 4\) and \(5 > 1\) --> \(3 - 5 < 4 - 1\).
Hope it helps.
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