Workers at a wildlife center plan a new habitat for meerkat The habitat must include at least \( 6.5 \mathrm{~m}^{2} \) of space for each meerkat. The area of the habitat is \( 78 \mathrm{~m}^{2} \). How many meerkats can the habitat hold? Write, solve, and graph an inequality to find the'possible numbers.of.meerkats. Show your work.

To determine how many meerkats can be accommodated in the habitat, we can set up an inequality based on the given area requirements. Let \( x \) represent the number of meerkats. Each meerkat requires \( 6.5 \mathrm{~m}^{2} \), so the total area needed for \( x \) meerkats is \( 6.5x \). Given that the total area of the habitat is \( 78 \mathrm{~m}^{2} \), we can write the inequality: \[ 6.5x \leq 78 \] Now, to solve for \( x \), we divide both sides of the inequality by \( 6.5 \): \[ x \leq \frac{78}{6.5} \\ x \leq 12 \] Thus, the habitat can hold a maximum of 12 meerkats. To graph this inequality, you would draw a number line and mark the point 12. Since the inequality is "less than or equal to," you would shade everything to the left of 12, including the point 12 itself (often represented with a closed circle). So, the solution is \( x \) can be any whole number from 0 up to 12 meerkats. Now, let's summarize the key points: - **Number of meerkats that can fit**: 12. - **Graph**: A number line showing all integer values from 0 to 12, closed at 12. ### Problem-Solving Tips & Common Mistakes: When working with inequalities, a common mistake is to incorrectly change the direction of the inequality sign while solving. Remember that you only reverse the inequality when you multiply or divide by a negative number! Also, always pay attention to units; make sure that your measurements are consistent. ### Real-World Application: Understanding how to efficiently calculate space requirements has real-world implications in wildlife conservation and habitat management. By ensuring adequate living space for animals, wildlife centers can promote healthier, happier animals that thrive in their environments. Whether designing new habitats or optimizing existing ones for animal care, these calculations help ensure the well-being of precious wildlife!