To determine which points are solutions to the inequality [tex]\( -x - 2y > 3 \)[/tex], we need to evaluate each point individually and see if the inequality holds true. Let's go through each of the given points one by one.
### Point (A) [tex]\((-1, -2)\)[/tex]
Substitute [tex]\( x = -1 \)[/tex] and [tex]\( y = -2 \)[/tex] into the inequality:
[tex]\[
-x - 2y > 3
\][/tex]
[tex]\[
-(-1) - 2(-2) > 3
\][/tex]
[tex]\[
1 + 4 > 3
\][/tex]
[tex]\[
5 > 3
\][/tex]
This is true. Hence, the point [tex]\( (-1, -2) \)[/tex] satisfies the inequality.
### Point (B) [tex]\((1, -2)\)[/tex]
Substitute [tex]\( x = 1 \)[/tex] and [tex]\( y = -2 \)[/tex] into the inequality:
[tex]\[
-x - 2y > 3
\][/tex]
[tex]\[
-(1) - 2(-2) > 3
\][/tex]
[tex]\[
-1 + 4 > 3
\][/tex]
[tex]\[
3 > 3
\][/tex]
This is false since 3 is not greater than 3. Hence, the point [tex]\( (1, -2) \)[/tex] does not satisfy the inequality.
### Point (C) [tex]\((-2, -1)\)[/tex]
Substitute [tex]\( x = -2 \)[/tex] and [tex]\( y = -1 \)[/tex] into the inequality:
[tex]\[
-x - 2y > 3
\][/tex]
[tex]\[
-(-2) - 2(-1) > 3
\][/tex]
[tex]\[
2 + 2 > 3
\][/tex]
[tex]\[
4 > 3
\][/tex]
This is true. Hence, the point [tex]\( (-2, -1) \)[/tex] satisfies the inequality.
### Point (D) [tex]\((2, -4)\)[/tex]
Substitute [tex]\( x = 2 \)[/tex] and [tex]\( y = -4 \)[/tex] into the inequality:
[tex]\[
-x - 2y > 3
\][/tex]
[tex]\[
-(2) - 2(-4) > 3
\][/tex]
[tex]\[
-2 + 8 > 3
\][/tex]
[tex]\[
6 > 3
\][/tex]
This is true. Hence, the point [tex]\( (2, -4) \)[/tex] satisfies the inequality.
### Conclusion
The points that satisfy the inequality [tex]\( -x - 2y > 3 \)[/tex] are:
- [tex]\((-1, -2)\)[/tex]
- [tex]\((-2, -1)\)[/tex]
- [tex]\((2, -4)\)[/tex]
Thus, the correct points are:
(A) [tex]\((-1, -2)\)[/tex]
(C) [tex]\((-2, -1)\)[/tex]
(D) [tex]\((2, -4)\)[/tex]
