To determine which points are solutions to the linear inequality [tex]\( y < 0.5x + 275 \)[/tex], we need to evaluate each point separately and see if it satisfies the inequality.
Let's go through each point:
1. Point [tex]\((-3, -2)\)[/tex]:
[tex]\[
y = -2 \quad \text{and} \quad 0.5x + 275 = 0.5(-3) + 275 = -1.5 + 275 = 273.5
\][/tex]
Check if [tex]\( -2 < 273.5 \)[/tex]:
[tex]\[
-2 \text{ is indeed less than } 273.5 \quad \text{(True)}
\][/tex]
So, [tex]\((-3, -2)\)[/tex] satisfies the inequality.
2. Point [tex]\((-2, 1)\)[/tex]:
[tex]\[
y = 1 \quad \text{and} \quad 0.5x + 275 = 0.5(-2) + 275 = -1 + 275 = 274
\][/tex]
Check if [tex]\( 1 < 274 \)[/tex]:
[tex]\[
1 \text{ is indeed less than } 274 \quad \text{(True)}
\][/tex]
So, [tex]\((-2, 1)\)[/tex] satisfies the inequality.
3. Point [tex]\((-1, -2)\)[/tex]:
[tex]\[
y = -2 \quad \text{and} \quad 0.5x + 275 = 0.5(-1) + 275 = -0.5 + 275 = 274.5
\][/tex]
Check if [tex]\( -2 < 274.5 \)[/tex]:
[tex]\[
-2 \text{ is indeed less than } 274.5 \quad \text{(True)}
\][/tex]
So, [tex]\((-1, -2)\)[/tex] satisfies the inequality.
4. Point [tex]\((-1, 2)\)[/tex]:
[tex]\[
y = 2 \quad \text{and} \quad 0.5x + 275 = 0.5(-1) + 275 = -0.5 + 275 = 274.5
\][/tex]
Check if [tex]\( 2 < 274.5 \)[/tex]:
[tex]\[
2 \text{ is indeed less than } 274.5 \quad \text{(True)}
\][/tex]
So, [tex]\((-1, 2)\)[/tex] satisfies the inequality.
5. Point [tex]\((1, -2)\)[/tex]:
[tex]\[
y = -2 \quad \text{and} \quad 0.5x + 275 = 0.5(1) + 275 = 0.5 + 275 = 275.5
\][/tex]
Check if [tex]\( -2 < 275.5 \)[/tex]:
[tex]\[
-2 \text{ is indeed less than } 275.5 \quad \text{(True)}
\][/tex]
So, [tex]\((1, -2)\)[/tex] satisfies the inequality.
Based on this evaluation, all the given points satisfy the inequality [tex]\( y < 0.5x + 275 \)[/tex]. Therefore, any three of these points can be selected as solutions to the inequality:
Three valid options could be:
1. [tex]\((-3, -2)\)[/tex]
2. [tex]\((-2, 1)\)[/tex]
3. [tex]\((-1, 2)\)[/tex]
