Solve the absolute value inequality |x|<1 Select the correct choice and, if necessary, fill in the answer boxes to complete your choice. A. The solution set is x|-□ . B. The solution is the empty set.

Analyze the absolute value inequality: The given inequality is $$|x| < 1$$$$|x|<1$$. This inequality represents all values of $$x$$$$x$$ whose distance from 0 is less than 1.

Apply the definition of absolute value inequalities: The inequality $$|x| < a$$$$|x|<a$$ is equivalent to $$-a < x < a$$$$-a<x<a$$. This is a fundamental property of absolute values.

Solve the inequality: Applying this property to our inequality, $$|x| < 1$$$$|x|<1$$, we get $$-1 < x < 1$$$$-1<x<1$$. This means $$x$$$$x$$ must lie between -1 and 1.

Express the solution set: Therefore, the solution set is $$\{x | -1 < x < 1\}$$$$\{x|-1<x<1\}$$. This set notation describes all real numbers $$x$$$$x$$ that are strictly greater than -1 and strictly less than 1.