Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A 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].
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.