To represent the weekend schedule constraints mathematically, we need to express each condition as an inequality involving [tex]\( v \)[/tex] and [tex]\( h \)[/tex], where [tex]\( v \)[/tex] is the number of hours spent playing video games and [tex]\( h \)[/tex] is the number of hours spent on homework.
Let's break down the constraints given in the problem:
1. You want to spend less than 2 hours playing video games:
[tex]\[ v < 2 \][/tex]
2. You must spend at least 1.5 hours on homework:
[tex]\[ h \geq 1.5 \][/tex]
3. You can spend at most 8 hours in total on video games and homework combined:
[tex]\[ v + h \leq 8 \][/tex]
4. Both [tex]\( v \)[/tex] and [tex]\( h \)[/tex] must be non-negative since you cannot spend negative hours on either activity:
[tex]\[ v \geq 0 \][/tex]
[tex]\[ h \geq 0 \][/tex]
Putting all these conditions together, we get the system of inequalities:
[tex]\[
\begin{array}{l}
v < 2 \\
h \geq 1.5 \\
v + h \leq 8 \\
v \geq 0 \\
h \geq 0
\end{array}
\][/tex]
Among the provided options, the correct system of equations representing this situation is:
[tex]\[
\begin{array}{l}
v < 2 \\
h \geq 1.5 \\
v + h \leq 8 \\
v \geq \\
h \geq 0
\end{array}
\][/tex]
