To determine the correct compound inequality representing the number of ounces of clay, [tex]\( c \)[/tex], that Elisa uses to make one vase of either size, let's carefully examine the conditions provided for the small and large vases:
1. For a small vase, Elisa uses no more than 4.5 ounces of clay.
- This means [tex]\( c \)[/tex] is at most 4.5, or [tex]\( c \leq 4.5 \)[/tex].
2. For a large vase, Elisa uses at least 12 ounces of clay.
- This means [tex]\( c \)[/tex] is at least 12, or [tex]\( c \geq 12 \)[/tex].
We need to combine these two conditions using "or" because the amount of clay used to make a vase can fall into either category (small or large). Thus, the compound inequality should represent [tex]\( c \leq 4.5 \)[/tex] or [tex]\( c \geq 12 \)[/tex].
Combining these inequalities, we get:
[tex]\[ c \leq 4.5 \text{ or } c \geq 12 \][/tex]
So, the correct compound inequality is:
[tex]\[ c \leq 4.5 \text{ or } c \geq 12 \][/tex]
