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Which of the following inequalities is an algebraic expression for the shaded part of the number line above?
  • a)
    |x -6| ≤ 3
  • b)
    |x + 6| ≤ 3
  • c)
    |x -6| ≥ 3
  • d)
    |x -3| < 6
  • e)
    |x + 3| > 6
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Which of the following inequalities is an algebraic expression for the...
This is a Reverse Logic question. So let us follow the usual process to solve it.
Step 1: First of all, we find the mid-point of the given solution set. That is, we find the point around which the solution set is symmetrical.
The mid-point here is (-9 -3)/2 = -6
So a = -6
Step 2: We find the distance of either end-point from the mid-point.
The distance of -3 from -6 is 3 units.
So, b = 3 units
Step 3: We insert the appropriate sign of inequality between |x -(-6)| and 3.
The shaded portion represents the numbers whose distance from -6 is less than 3 units. We also observe that at the end points we have FULL CIRCLES.
Therefore, the absolute value expression for the given number line representation is:
|x + 6| ≤ 3
Correct Answer: B
This question is part of UPSC exam. View all GMAT courses
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Which of the following inequalities is an algebraic expression for the shaded part of the number line above?a)|x -6| ≤ 3b)|x + 6| ≤ 3c)|x -6| ≥ 3d)|x -3| < 6e)|x + 3| > 6Correct answer is option 'B'. Can you explain this answer?
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