Question

Which of the following is the solution to |x|+19<=3

A. x<=-16
B. no solution
C. all values are solutions
D. x<=-16 and x=>16

Answer 1

B

Explanation:

Consider the inequality
`|x|+19\le 3`

Subtract 19 from both sides of inequality:

`|x|+19-19\le 3-19\\ \\|x|\le -16`

Since the absolute value of the variable x is always non-negative (by definition), then the absolute value of x cannot be less or equal to -16. This means the inequality has no solutions.