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If a constraint-based set is defined as {x | x is a real number and x^2 < 4},

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Question: If a constraint-based set is defined as {x | x is a real number and x^2 < 4}, what is the range of x?

Options:

  1. (-2, 2)
  2. [0, 2]
  3. (-∞, ∞)
  4. (0, 4)

Correct Answer: (-2, 2)

Solution: 

The inequality x^2 < 4 implies that x must be between -2 and 2, hence the range is (-2, 2).

If a constraint-based set is defined as {x | x is a real number and x^2 < 4},

Practice Questions

Q1
If a constraint-based set is defined as {x | x is a real number and x^2 < 4}, what is the range of x?
  1. (-2, 2)
  2. [0, 2]
  3. (-∞, ∞)
  4. (0, 4)

Questions & Step-by-Step Solutions

If a constraint-based set is defined as {x | x is a real number and x^2 < 4}, what is the range of x?
  • Step 1: Start with the inequality given in the question: x^2 < 4.
  • Step 2: To solve this inequality, we need to find the values of x that make it true.
  • Step 3: Rewrite the inequality: x^2 < 4 can be rewritten as -2 < x < 2.
  • Step 4: This means that x can take any value between -2 and 2, but not including -2 and 2 themselves.
  • Step 5: Therefore, the range of x is expressed in interval notation as (-2, 2).
  • Inequalities – Understanding how to solve and interpret inequalities involving real numbers.
  • Interval Notation – Knowledge of how to express ranges of values using interval notation.
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