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].
