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.
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].
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].
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Find clear answers at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.