Answer:
[tex]0 \leq x \leq 100[/tex]
0, 40, and 80 are the values that work for this compound inequality.
Step-by-step explanation:
To create a compound inequality, we have to examine the conditions for [tex]x[/tex] to work.
Since [tex]x[/tex] can not be below 0° C, that means that [tex]x[/tex] must be greater than or equal to 0.
Which is represented as [tex]x\geq 0[/tex], or [tex]0\leq x[/tex].
Since [tex]x[/tex] can not be above 100° C, that means [tex]x[/tex] must be less than 100.
Which is represented as [tex]x \leq 100[/tex].
We can combine both inequalities into one, where [tex]x[/tex] is shared between the two. This creates [tex]0\leq x \leq 100[/tex].
Let's test each value of [tex]x[/tex] .
0 is equal to 0 and less than 100, so it works.
40 is greater than 0 and less than 100, so it works.
80 is greater than 0 and less than 100, so it works.
120 is greater than 0 and greater than 100, so it doesn't work.
160 is greater than 0 and greater than 100, so it doesn't work.
Hope this helped!
