Questions: Solve the inequality. [ 4-8 x<-13 ] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is a finite set . (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.) B. The solution set is an infinite set . (Simplify your answer. Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) C. The solution set is varnothing.

Solution Steps

To solve the inequality \(|4 - 8x| < -13\), we need to consider the properties of absolute values. The absolute value of any expression is always non-negative, meaning it is always greater than or equal to zero. Therefore, an inequality of the form \(|expression| < negative\_number\) has no solution because an absolute value cannot be less than a negative number. Thus, the solution set is the empty set, \(\varnothing\).

The given inequality is \(|4 - 8x| < -13\). The absolute value of any expression is always non-negative, meaning it is always greater than or equal to zero. Therefore, an inequality of the form \(|expression| < \text{negative number}\) has no solution because an absolute value cannot be less than a negative number.

Since the inequality \(|4 - 8x| < -13\) is impossible to satisfy, the solution set is the empty set, denoted by \(\varnothing\).

Final Answer