Question

Y greater than or equal to |x| + 3

which of the following is NOT a solution of the inequality

Answer 1

(-3,0) would not be a solution to the inequality.

Answer 2

We conclude that the point (-3, 0) does NOT satisfy the inequality.

Explanation:

Given the expression

`y\ge \:\left|x\right|+3\:\:\:\:`

putting x = -3 and y = 6

`6\ge \left|-3\right|+3\:\:\:`

Apply absolute rule: |-a| = a

`6\ge \:6`

TRUE

Thus, the point (-3, 6) satisfies the inequality.

Given the expression

`y\ge \:\left|x\right|+3\:\:\:\:`

putting x = 0 and y = 4

`4\ge \left|0\right|+3`

Apply absolute rule: |a| = a, a≥0

`4\ge \:3`

TRUE

Thus, the point (0, 4) satisfies the inequality.

Given the expression

`y\ge \:\left|x\right|+3\:\:\:\:`

putting x = -3 and y = 0

`0\ge \left|-3\right|+3\:\:\:`

Apply absolute rule: |-a| = a

`0\ge \:6`

FALSE

Thus, the point (-3, 0) does NOT satisfy the inequality.

Therefore, we conclude that the point (-3, 0) does NOT satisfy the inequality.