To determine which answer choices are solutions to the inequality [tex]\(1.5x + 3.75 \geq 5.5\)[/tex], we will evaluate each given choice one by one.
1. Evaluate for [tex]\( x = -1 \)[/tex]:
[tex]\[
1.5(-1) + 3.75 \geq 5.5 \quad \Rightarrow \quad -1.5 + 3.75 \geq 5.5 \quad \Rightarrow \quad 2.25 \geq 5.5
\][/tex]
This is not true. Hence, [tex]\( x = -1 \)[/tex] is not a solution.
2. Evaluate for [tex]\( x = 0 \)[/tex]:
[tex]\[
1.5(0) + 3.75 \geq 5.5 \quad \Rightarrow \quad 0 + 3.75 \geq 5.5 \quad \Rightarrow \quad 3.75 \geq 5.5
\][/tex]
This is not true. Hence, [tex]\( x = 0 \)[/tex] is not a solution.
3. Evaluate for [tex]\( x = 1 \)[/tex]:
[tex]\[
1.5(1) + 3.75 \geq 5.5 \quad \Rightarrow \quad 1.5 + 3.75 \geq 5.5 \quad \Rightarrow \quad 5.25 \geq 5.5
\][/tex]
This is not true. Hence, [tex]\( x = 1 \)[/tex] is not a solution.
4. Evaluate for [tex]\( x = 1.5 \)[/tex]:
[tex]\[
1.5(1.5) + 3.75 \geq 5.5 \quad \Rightarrow \quad 2.25 + 3.75 \geq 5.5 \quad \Rightarrow \quad 6.0 \geq 5.5
\][/tex]
This is true. Hence, [tex]\( x = 1.5 \)[/tex] is a solution.
Based on the evaluations, the only value that satisfies the inequality [tex]\(1.5x + 3.75 \geq 5.5\)[/tex] is:
[tex]\[
\boxed{1.5}
\][/tex]
