Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

Which of the following points is a solution of the inequality [tex]y \ \textless \ -|x|[/tex]?

A. [tex]\((1,0)\)[/tex]
B. [tex]\((1,-1)\)[/tex]
C. [tex]\((1,-2)\)[/tex]

Sagot :

GinnyAnswer
To determine which of the points is a solution to the inequality [tex]\( y < -|x| \)[/tex], we need to check each point against this inequality step-by-step.

### Check Point (1, 0)
1. For [tex]\( (1, 0) \)[/tex]:
- [tex]\( x = 1 \)[/tex]
- [tex]\( y = 0 \)[/tex]
- Calculate [tex]\( -|x| \)[/tex]: [tex]\( -|1| = -1 \)[/tex]
- Check if [tex]\( y < -|x| \)[/tex]: [tex]\( 0 < -1 \)[/tex]
- This is false.

### Check Point (1, -1)
2. For [tex]\( (1, -1) \)[/tex]:
- [tex]\( x = 1 \)[/tex]
- [tex]\( y = -1 \)[/tex]
- Calculate [tex]\( -|x| \)[/tex]: [tex]\( -|1| = -1 \)[/tex]
- Check if [tex]\( y < -|x| \)[/tex]: [tex]\( -1 < -1 \)[/tex]
- This is false.

### Check Point (1, -2)
3. For [tex]\( (1, -2) \)[/tex]:
- [tex]\( x = 1 \)[/tex]
- [tex]\( y = -2 \)[/tex]
- Calculate [tex]\( -|x| \)[/tex]: [tex]\( -|1| = -1 \)[/tex]
- Check if [tex]\( y < -|x| \)[/tex]: [tex]\( -2 < -1 \)[/tex]
- This is true.

After evaluating all the points, we see that the point [tex]\((1, -2)\)[/tex] satisfies the inequality [tex]\( y < -|x| \)[/tex].

Therefore, the point which is a solution of the inequality [tex]\( y < -|x| \)[/tex] is [tex]\((1, -2)\)[/tex].
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.