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Which of the following points is not a solution of the inequality y ≥ |x| + 3? (-3, 0) (-3, 6) (0, 4)

Answer :

frijole123
If y has to be greater than or equal to |x| + 3, we can use the points to find which is not a solution.

(-3,0):   0 ≥ |-3| + 3  →  0 ≥ 6

This is not a solution to the inequality, thus (-3,0) would be your answer.

  From the given options, (-3, 0) is not the solution of the inequality y ≥ |x| + 3.

  Inequality given in the question → y ≥ |x| + 3

Although graphically, all the points lying in the common region above the lines y ≥ x + 3 and y ≥ -x + 3 will be the solutions of the inequality y ≥ |x| + 3.

We can find the points which lie in the solution region algebraically also.

If a point satisfies the inequality, point will be the solution.

For (-3, 0),

y ≥ |x| + 3

0 ≥ |-3| + 3

0 ≥ 6

False.

For (-3, 6),

y ≥ |x| + 3

6 ≥ |-3| + 3

6 ≥ 6

True.

For (0, 4),

y ≥ |x| + 3

4 ≥ |0| + 3

4 ≥ 3

True.

   Therefore, (-3, 0) is not the solution of the given inequality y ≥ |x| + 3.

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