Question
Which of the following is a solution of \( y>|x|-6 \) ? \( (5,-1) \) \( (-1,-5) \) \( (-5,1) \)
Ask by Hodges Lowe. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The ordered pair (-5, 1) satisfies the inequality \( y > |x| - 6 \).
Solution
To determine which ordered pair satisfies the inequality y > |x| – 6, we'll substitute the coordinates from each option into the inequality.
1. For (5, -1):
|5| – 6 = 5 – 6 = -1.
Check: -1 > -1? This is false since -1 is not greater than -1.
2. For (-1, -5):
|–1| – 6 = 1 – 6 = -5.
Check: -5 > -5? This is false for the same reason.
3. For (-5, 1):
|–5| – 6 = 5 – 6 = -1.
Check: 1 > -1? This is true.
Thus, the ordered pair (-5, 1) is the solution.
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Simplify this solution Bonus Knowledge
To determine which of the given points is a solution of the inequality \( y>|x|-6 \), we can substitute the coordinates of each point into the inequality. 1. For the point \( (5,-1) \): \[ -1 > |5| - 6 \implies -1 > 5 - 6 \implies -1 > -1 \text{ (false)} \] 2. For the point \( (-1,-5) \): \[ -5 > |-1| - 6 \implies -5 > 1 - 6 \implies -5 > -5 \text{ (false)} \] 3. For the point \( (-5,1) \): \[ 1 > |-5| - 6 \implies 1 > 5 - 6 \implies 1 > -1 \text{ (true)} \] The point \( (-5, 1) \) is a solution of the inequality \( y>|x|-6 \).
