If |2x + 1| <= 0, then
A) x must be less than or equal to - 1/2
B) x must be equal to - 1/2
C) x must be larger than - 1/2
D) x could be 1/2
E) x doesn't exist
OA: B
I can develop the inequality in order to reach x <= - 1/2 or x >= - 1/2. I just don't understand the official answer.
Thanks,
Fambrini
Any help, please?
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An absolute value can never be negative.fambrini wrote:If |2x + 1| <= 0, then
A) x must be less than or equal to - 1/2
B) x must be equal to - 1/2
C) x must be larger than - 1/2
D) x could be 1/2
E) x doesn't exist
OA: B
I can develop the inequality in order to reach x <= - 1/2 or x >= - 1/2. I just don't understand the official answer.
Thanks,
Fambrini
Thus, it is not possible that |2x+1| < 0.
It is only possible that |2x+1| = 0.
|2x+1| = 0 if 2x+1 = 0:
2x+1 = 0
2x = -1
x = -1/2.
The correct answer is B.
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Hi fambrini,
Before working through any of the 'steps' in this question, you should note the main 'concept' involved:
We're dealing with an Absolute Value - and the result of any Absolute Value calculation can NEVER be negative. It can be 0 or it can be positive. Thus, when we're given the following inequality...
|2X + 1| <= 0
... we should note the fact that the absolute value is 'less than or equal to 0.' Mathematically, it CANNOT be less than 0, so it MUST EQUAL 0. Knowing that, we have just one small calculation to get to the correct answer...
2X + 1 = 0
2X = -1
X = -1/2
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
Before working through any of the 'steps' in this question, you should note the main 'concept' involved:
We're dealing with an Absolute Value - and the result of any Absolute Value calculation can NEVER be negative. It can be 0 or it can be positive. Thus, when we're given the following inequality...
|2X + 1| <= 0
... we should note the fact that the absolute value is 'less than or equal to 0.' Mathematically, it CANNOT be less than 0, so it MUST EQUAL 0. Knowing that, we have just one small calculation to get to the correct answer...
2X + 1 = 0
2X = -1
X = -1/2
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
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This is an interesting question because the absolute value of anything cannot ever be LESS THAN ZERO. Thus, we can rewrite the equation as |2x + 1| = 0 and solve for x. We note that the absolute value of an expression can only equal zero if the expression itself is equal to zero.fambrini wrote:If |2x + 1| <= 0, then
A) x must be less than or equal to - 1/2
B) x must be equal to - 1/2
C) x must be larger than - 1/2
D) x could be 1/2
E) x doesn't exist
OA: B
2x + 1 = 0
2x = -1
x = -(1/2)
Answer: B
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When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:fambrini wrote:If |2x + 1| < 0, then
A) x must be less than or equal to - 1/2
B) x must be equal to - 1/2
C) x must be larger than - 1/2
D) x could be 1/2
E) x doesn't exist
Rule #1: If |something| < k, then -k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is not negative
So, when we apply rule #1, -0 < 2x + 1 < 0
That's odd!
2x + 1 is greater than or equal to 0 AND less than or equal to 0
So, it MUST be the case that 2x + 1 = 0
Solve to get x = 1/2
Answer: B
RELATED VIDEO
- Inequalities and absolute value: https://www.gmatprepnow.com/module/gmat ... /video/985
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Let's do it conceptually.
|a - b| = 0 means "the distance from a to b is 0".
|a - b| ≤ 0 means "the distance from a to b is LESS THAN or EQUAL TO 0".
Obviously you can't have a distance that's less than 0, so
|2x + 1| ≤ 0 must really be
|2x + 1| = 0
and from there the problem is a cinch!
|2x + 1| = 0 means "the distance from 2x to -1 is 0", or 2x = -1, or x = -1/2.
|a - b| = 0 means "the distance from a to b is 0".
|a - b| ≤ 0 means "the distance from a to b is LESS THAN or EQUAL TO 0".
Obviously you can't have a distance that's less than 0, so
|2x + 1| ≤ 0 must really be
|2x + 1| = 0
and from there the problem is a cinch!
|2x + 1| = 0 means "the distance from 2x to -1 is 0", or 2x = -1, or x = -1/2.
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And not to editorialize too much, but the CONCEPT of absolute value as distance is something I think more students ought to learn and remember: it can rescue you from some pretty thick algebraic fog!