Final answer:
The solutions of the inequality |x|≤ 19 is the interval [-19, 19].
Step-by-step explanation:
The solution of the inequality |x|≤ 19 is the interval [-19, 19].
When we have an absolute value inequality, we break it into two separate inequalities: one with a positive sign and one with a negative sign.
For the positive sign, we have x≤19. For the negative sign, we have -x≤19. Solving both of these inequalities, we get -19≤x≤19.
Therefore, the solution to the inequality |x|≤ 19 is the interval [-19, 19].