Discover how IDNLearn.com can help you find the answers you need quickly and easily. Get accurate answers to your questions from our community of experts who are always ready to provide timely and relevant solutions.

Which ordered pair is a solution to the following linear inequality?

[tex]\[ y \ \textless \ x + 1 \][/tex]

A. [tex]\((-4, -1)\)[/tex]

B. [tex]\((-2, 4)\)[/tex]

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

D. [tex]\((-3, 0)\)[/tex]


Sagot :

To determine which ordered pairs satisfy the inequality [tex]\(y < x + 1\)[/tex], let's evaluate each of the given pairs.

1. Consider the pair [tex]\((-4, -1)\)[/tex]:
- Substitute [tex]\(x = -4\)[/tex] and [tex]\(y = -1\)[/tex] into the inequality:
[tex]\[ y < x + 1 \implies -1 < -4 + 1 \][/tex]
- Simplify the right side:
[tex]\[ -1 < -3 \][/tex]
- This inequality is not true because [tex]\(-1\)[/tex] is not less than [tex]\(-3\)[/tex].

2. Consider the pair [tex]\((-2, 4)\)[/tex]:
- Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = 4\)[/tex] into the inequality:
[tex]\[ y < x + 1 \implies 4 < -2 + 1 \][/tex]
- Simplify the right side:
[tex]\[ 4 < -1 \][/tex]
- This inequality is not true because [tex]\(4\)[/tex] is not less than [tex]\(-1\)[/tex].

3. Consider the pair [tex]\((1, -2)\)[/tex]:
- Substitute [tex]\(x = 1\)[/tex] and [tex]\(y = -2\)[/tex] into the inequality:
[tex]\[ y < x + 1 \implies -2 < 1 + 1 \][/tex]
- Simplify the right side:
[tex]\[ -2 < 2 \][/tex]
- This inequality is true because [tex]\(-2\)[/tex] is less than [tex]\(2\)[/tex].

4. Consider the pair [tex]\((-3, 0)\)[/tex]:
- Substitute [tex]\(x = -3\)[/tex] and [tex]\(y = 0\)[/tex] into the inequality:
[tex]\[ y < x + 1 \implies 0 < -3 + 1 \][/tex]
- Simplify the right side:
[tex]\[ 0 < -2 \][/tex]
- This inequality is not true because [tex]\(0\)[/tex] is not less than [tex]\(-2\)[/tex].

From our evaluation, the ordered pair [tex]\((1, -2)\)[/tex] is the only pair that satisfies the inequality [tex]\(y < x + 1\)[/tex]. Therefore, the solution is:

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