To determine the greatest number of 70-kilogram crates that can be loaded onto the shipping container, we need to represent the situation with an inequality.
You start with the maximum weight capacity of the container, which is 23,500 kilograms. From this weight, we need to subtract the weight of the already-loaded shipments (13,000 kilograms). The remaining weight capacity is the difference between the maximum capacity and the weight of the already-loaded shipments:
Remaining weight capacity: \( 23500 - 13000 = 10500 \) kilograms
Since each crate weighs 70 kilograms, the total weight of \( x \) crates is \( 70x \). Therefore, the inequality that represents this situation becomes:
\[ 70x \leq 10500 \]
Now, if we rewrite this to reflect the situation presented in the question, we can express it as follows:
\[ 70(x) + 13000 \leq 23500 \]
This means that the weight of the crates plus the weight of the already-loaded shipments cannot exceed the container's maximum weight capacity.
Among the options provided, the correct inequality is:
70(x) + 13000 ≤ 23500
So the answer is:
70, left parenthesis, x, plus, 13000, right parenthesis, is less than or equal to, 23500 (70(x) + 13000 ≤ 23500).