Problem Solving

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

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

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.

2x + 1 = 0

2x = -1

x = -(1/2)

Answer: B

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

When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
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