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

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asked Aug 1, 2021 57.7k views

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Jesenko · Answer 1 · 2021-08-05T05:18:39+0000

Answer:

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.

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

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