To solve the problem, let's define the inequality step by step.

Problem Breakdown:

1. The greatest weight the container can hold is 27,500 kilograms.
2. There is already a shipment loaded that weighs 14,900 kilograms.
3. Each crate weighs 120 kilograms.
4. We are asked to determine the number of crates, $x$, that can be loaded into the container.

Step 1: Define the Total Weight

The total weight in the container is the sum of the existing shipment (14,900 kilograms) and the weight of the additional crates. The weight of the additional crates is $120 \times x$, where $x$ is the number of crates.

So, the total weight is: $\text{Total Weight} = 14,900 + 120x$

Step 2: Set Up the Inequality

The total weight cannot exceed the maximum weight capacity of the container, which is 27,500 kilograms. Therefore, the inequality is: $14,900 + 120x \leq 27,500$

Step 3: Solve the Inequality

1. Subtract 14,900 from both sides: $120x \leq 27,500 - 14,900$ $120x \leq 12,600$

2. Divide both sides by 120: $x \leq \frac{12,600}{120}$ $x \leq 105$

Final Answer:

The inequality is $x \leq 105$. This means that the maximum number of 120-kilogram crates that can be loaded into the shipping container is 105.

If you have any questions or want further details, feel free to ask!

Here are 5 related questions to deepen your understanding:

1. How would the inequality change if the existing shipment weighed 10,000 kilograms instead?
2. What if the container's weight capacity was increased to 30,000 kilograms? How many crates could be loaded then?
3. How would you calculate the number of crates if the weight of each crate was 150 kilograms instead of 120 kilograms?
4. Can you represent the relationship between the number of crates and the total weight graphically?
5. What would the inequality be if there were no preloaded shipments?

Tip: When solving inequalities, always carefully track units to ensure consistent and accurate calculations.