Answered

Find answers to your questions faster and easier with IDNLearn.com. Join our interactive Q&A community and access a wealth of reliable answers to your most pressing questions.

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 :

GinnyAnsweridn
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]
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com provides the answers you need. Thank you for visiting, and see you next time for more valuable insights.