Let's formulate and solve the inequality:

Step 1: Understand the problem

• The maximum weight the container can hold is 27,500 kg.
• There are already 14,900 kg loaded in the container.
• Each crate weighs 120 kg, and the goal is to determine the maximum number of crates ($x$) that can still be added without exceeding the container's weight limit.

Step 2: Formulate the inequality

The total weight in the container after adding the crates must not exceed $27,500$ kg: $14900 + 120x \leq 27500$

Step 3: Solve the inequality

1. Subtract $14,900$ from both sides: $120x \leq 27500 - 14900$ $120x \leq 12600$

2. Divide by 120 to isolate $x$: $x \leq \frac{12600}{120}$ $x \leq 105$

Step 4: Interpret the solution

The maximum number of 120-kilogram crates that can be loaded is $\mathbf{105}$.

Final Answer:

The inequality is: $14900 + 120x \leq 27500$ And the solution is: $x \leq 105$

This means up to 105 crates can be added to the container.

Would you like more details or assistance with related problems? Here are some related questions you might explore:

1. How would the inequality change if the container's weight limit were higher or lower?
2. What happens if each crate weighs a different amount, such as 150 kg?
3. How can you check if the solution satisfies the inequality?
4. What if 500 kg were removed from the existing load before adding crates?
5. How would you graph this inequality to visualize the solution?

Tip: Always double-check your final answer by substituting it back into the inequality!