Which of the following points is a solution of the inequality $$ y

Question

Which of the following points is a solution of the inequality $$ y<|x-2| $$ ? $$ (2,0) $$ $$ (2,1) $$ $$ (-2,0) $$

UpStudy AI · Accepted Answer

To determine which point satisfies the inequality y < |x - 2|, substitute each point into the inequality.

For (2,0):
 y = 0 and x = 2.
 Inequality: 0 < |2 - 2| = |0| = 0.
 Since 0 is not less than 0, (2,0) does not satisfy the inequality.

For (2,1):
 y = 1 and x = 2.
 Inequality: 1 < |2 - 2| = |0| = 0.
 Since 1 is not less than 0, (2,1) does not satisfy the inequality.

For (-2,0):
 y = 0 and x = -2.
 Inequality: 0 < |(-2) - 2| = |-4| = 4.
 Since 0 is less than 4, (-2,0) satisfies the inequality.

Thus, the point (-2,0) is a solution of the inequality y < |x-2|.
The point (-2,0) satisfies the inequality $$ y < |x - 2| $$.

Which of the following points is a solution of the inequality \( y<|x-2| \) ? \( (2,0) \) \( (2,1) \) \( (-2,0) \)