Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Which points are solutions to the linear inequality [tex]y \ \textless \ 0.5x + 2[/tex]? Select three options:

A. [tex]\((-3, -2)\)[/tex]

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

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

D. [tex]\((-1, 2)\)[/tex]

E. [tex]\((1, -2)\)[/tex]

Sagot :

GinnyAnswer
Let's examine each point to determine if it satisfies the inequality [tex]\( y < 0.5x + 2 \)[/tex].

1. Point [tex]\((-3, -2)\)[/tex]:
- Substitute [tex]\( x = -3 \)[/tex] and [tex]\( y = -2 \)[/tex] into the inequality:
[tex]\[ -2 < 0.5(-3) + 2 \][/tex]
[tex]\[ -2 < -1.5 + 2 \][/tex]
[tex]\[ -2 < 0.5 \][/tex]
This inequality is true. Therefore, [tex]\((-3, -2)\)[/tex] is a solution.

2. Point [tex]\((-2, 1)\)[/tex]:
- Substitute [tex]\( x = -2 \)[/tex] and [tex]\( y = 1 \)[/tex] into the inequality:
[tex]\[ 1 < 0.5(-2) + 2 \][/tex]
[tex]\[ 1 < -1 + 2 \][/tex]
[tex]\[ 1 < 1 \][/tex]
This inequality is not true because 1 is not less than 1. Therefore, [tex]\((-2, 1)\)[/tex] is not a solution.

3. Point [tex]\((-1, -2)\)[/tex]:
- Substitute [tex]\( x = -1 \)[/tex] and [tex]\( y = -2 \)[/tex] into the inequality:
[tex]\[ -2 < 0.5(-1) + 2 \][/tex]
[tex]\[ -2 < -0.5 + 2 \][/tex]
[tex]\[ -2 < 1.5 \][/tex]
This inequality is true. Therefore, [tex]\((-1, -2)\)[/tex] is a solution.

4. Point [tex]\((-1, 2)\)[/tex]:
- Substitute [tex]\( x = -1 \)[/tex] and [tex]\( y = 2 \)[/tex] into the inequality:
[tex]\[ 2 < 0.5(-1) + 2 \][/tex]
[tex]\[ 2 < -0.5 + 2 \][/tex]
[tex]\[ 2 < 1.5 \][/tex]
This inequality is not true because 2 is not less than 1.5. Therefore, [tex]\((-1, 2)\)[/tex] is not a solution.

5. Point [tex]\((1, -2)\)[/tex]:
- Substitute [tex]\( x = 1 \)[/tex] and [tex]\( y = -2 \)[/tex] into the inequality:
[tex]\[ -2 < 0.5(1) + 2 \][/tex]
[tex]\[ -2 < 0.5 + 2 \][/tex]
[tex]\[ -2 < 2.5 \][/tex]
This inequality is true. Therefore, [tex]\((1, -2)\)[/tex] is a solution.

Based on our analysis, the points that are solutions to the inequality [tex]\( y < 0.5x + 2 \)[/tex] are:

- [tex]\((-3, -2)\)[/tex]
- [tex]\((-1, -2)\)[/tex]
- [tex]\((1, -2)\)[/tex]
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.