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Which of the following inequalities is an algebraic expression for the shaded part of the number line above?
  • a)
    |x – 1| ≥ 2
  • b)
    |x+1| ≥ 2
  • c)
    |x -3| ≥ 4
  • d)
    |x+3| ≥ 4
  • e)
    |x+1| ≥ -3
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Which of the following inequalities is an algebraic expression for the...
Step 1: Question statement and Inferences
This is a Reverse Logic Inequality. Here, we are given the solution set of the inequality, and we are asked to determine the expression for the inequality. So, we will follow the process below to solve it:
Step 1: Plot the mid-point of the solution set on the number line. Mid-point = a
Step 2: Find the distance of either end-point from the mid-point. This distance =b
Step 3: Insert the appropriate sign of inequality between |x-a| and b
Step 2 & 3: Working with the answer choices and calculating the final answer
Let’s apply this process to the current problem:
Step 1: The mid-point of the solution set is -1. Thus, a = -1
Step 2: The distance of -3 from -1 = the distance of 1 from -1 = 2 units. Thus, b = 2
Step 3: Since points -3 and 1 are also included in the solution set (as indicated by the full circles at these two points), the correct inequality sign will be ≥ and not just >
So, the expression for the inequality is:
|x – (-1)| ≥ 2
That is, |x+1| ≥ 2
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Which of the following inequalities is an algebraic expression for the shaded part of the number line above?a)|x – 1| ≥ 2b)|x+1| ≥ 2c)|x -3| ≥ 4d)|x+3| ≥ 4e)|x+1| ≥ -3Correct answer is option 'B'. Can you explain this answer?
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