Express the set W = { x ∣ | x | < 1 } using interval notation.
To express the set W = { x ∣ | x | < 1 } using interval notation, we need to consider both the positive and negative values of x separately.
First, let's consider the positive values of x.
For |x| < 1, the positive values of x whose absolute value is less than 1 are all the values between -1 and 1. Since the inequality is strict (|x| < 1), we exclude the values -1 and 1 themselves.
Therefore, the interval for positive values of x would be (0, 1), which means x is greater than 0 and less than 1.
Next, let's consider the negative values of x.
For |x| < 1, the negative values of x whose absolute value is less than 1 are all the values between -1 and 1. Again, we exclude the values -1 and 1.
Therefore, the interval for negative values of x would be (-1, 0), which means x is greater than -1 and less than 0.
Finally, to express the set W = { x ∣ | x | < 1 } using interval notation, we combine the intervals for positive and negative values of x. The result is (-1, 0) U (0, 1).
In interval notation, the set W can be expressed as (-1, 0) U (0, 1).