Question

Which of the following is the solution to |x| + 55 < 1?

A. x ≤ -4
B. All values are solutions
C. x ≤ -4 and x ≥ -6
D. No solution

Answer 1

The inequality |x| + 55 < 1 leads to |x| < -54 after subtracting 55 from both sides. However, an absolute value cannot be negative, so there is no solution to this inequality.

This correct answer is D.

Step-by-step explanation:

The question is asking to solve the inequality |x| + 55 < 1. To find the solution, we will isolate the absolute value expression by subtracting 55 from both sides of the inequality:

|x| + 55 - 55 < 1 - 55

|x| < -54

By the definition of absolute value, |x| is the distance from 0 on the number line and cannot be negative, meaning that it is impossible for |x| to be less than -54. Therefore, there is no solution to the inequality since the absolute value of x cannot be less than zero.

This correct answer is D.