Pregunta
Which of the following points is not a solution of the inequality \( y \geq|x|+3 \) ? \( (0,4) \) \( (-3,0) \) \( (-3,6) \)
Ask by Vargas Owen. in the United States
Feb 25,2025
Solución de inteligencia artificial de Upstudy
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The point (-3, 0) is not a solution to the inequality \( y \geq|x|+3 \).
Solución
Let's test each point in the inequality y ≥ |x| + 3.
1. For (0, 4):
- |0| = 0
- Check: 4 ≥ 0 + 3, which is 4 ≥ 3 (true).
2. For (-3, 0):
- |-3| = 3
- Check: 0 ≥ 3 + 3, which is 0 ≥ 6 (false).
3. For (-3, 6):
- |-3| = 3
- Check: 6 ≥ 3 + 3, which is 6 ≥ 6 (true).
Therefore, the point (-3, 0) is not a solution to the inequality.
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To determine which point is not a solution to the inequality \( y \geq |x| + 3 \), we evaluate each point: 1. For \( (0,4) \): Substitute \( x = 0 \). Then \( |0| + 3 = 3 \). Since \( 4 \geq 3 \), this point is a solution. 2. For \( (-3,0) \): Substitute \( x = -3 \). Then \( |-3| + 3 = 6 \). Since \( 0 \geq 6 \) is false, this point is NOT a solution. 3. For \( (-3,6) \): Substitute \( x = -3 \) again. We find \( 6 \geq 6 \), so this point is a solution. Thus, the point \( (-3,0) \) is not a solution of the inequality \( y \geq |x| + 3 \).
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