We are tasked with writing and solving an inequality for the perimeter of a quadrilateral where the perimeter is less than or equal to 18.7 feet. The quadrilateral has side lengths of 4.1 feet, $x$ feet, 6.4 feet, and 4.9 feet.

Step 1: Write the inequality

The perimeter $P$ of the quadrilateral is the sum of the side lengths. Therefore, we can express the perimeter as: $P = 4.1 + x + 6.4 + 4.9$

Since the perimeter is less than or equal to 18.7 feet, we can set up the inequality as follows: $4.1 + x + 6.4 + 4.9 \leq 18.7$

Step 2: Simplify the inequality

First, combine the constants: $4.1 + 6.4 + 4.9 = 15.4$ Now, the inequality becomes: $15.4 + x \leq 18.7$

Step 3: Solve for $x$

To solve for $x$, subtract 15.4 from both sides: $x \leq 18.7 - 15.4$ $x \leq 3.3$

Final answer:

The possible values of $x$ must satisfy: $x \leq 3.3$

Conclusion:

The possible values of $x$ are any values less than or equal to 3.3 feet.

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Do you want further details or have any questions?

Here are 5 related questions to explore this topic further:

1. What would happen if one of the side lengths of the quadrilateral changed?
2. How would you set up an inequality if the perimeter had to be greater than a certain value?
3. Can you find the range of $x$ if the perimeter must be between 15 and 18.7 feet?
4. How do you determine the perimeter of polygons with more sides, such as pentagons or hexagons?
5. What if the perimeter was exactly 18.7 feet? How would that change the inequality?

Tip: When solving inequalities, always check if the inequality symbol flips direction when multiplying or dividing by a negative number.