If a set is defined by the constraints 'x is a real number and x^2 < 4', whic

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Question: If a set is defined by the constraints \'x is a real number and x^2 < 4\', which of the following intervals represents this set?

Options:

Correct Answer: (-2, 2)

Solution:

The interval (-2, 2) represents all real numbers whose square is less than 4.

If a set is defined by the constraints 'x is a real number and x^2 < 4', which of the following intervals represents this set?

If a set is defined by the constraints 'x is a real number and x^2 < 4', which of the following intervals represents this set?

Step 1: Understand the constraint 'x is a real number and x^2 < 4'. This means we are looking for all real numbers x whose square is less than 4.
Step 2: Rewrite the inequality x^2 < 4 in a different form. We can do this by taking the square root of both sides. The square root of 4 is 2.
Step 3: The inequality x^2 < 4 means that x must be between -2 and 2, but not including -2 and 2 themselves. This is because if x equals -2 or 2, then x^2 equals 4, which does not satisfy the inequality.
Step 4: Therefore, the solution can be expressed in interval notation as (-2, 2). This notation means all numbers greater than -2 and less than 2.

Inequalities – Understanding how to solve and interpret inequalities, particularly those involving squares of real numbers.
Interval Notation – Knowledge of how to express sets of numbers using interval notation, including open and closed intervals.