- Analyze the inequality \(4d > 24\) and identify that \(d\) is multiplied by 4.
- Choose the correct method to isolate \(d\), which is to divide both sides of the inequality by 4.
- Execute the division: \(\frac{4d}{4} > \frac{24}{4}\).
- Obtain the final solution: \(\boxed{d > 6}\).
Explanation
- Analyzing the Inequality
The inequality we are given is \(4d > 24\). Our goal is to isolate the variable \(d\) to find the set of values that satisfy this condition. In the expression \(4d\), the variable \(d\) is being multiplied by 4. To isolate \(d\), we need to perform the inverse operation, which is division. Dividing both sides of an inequality by a positive number is a valid operation that does not change the direction of the inequality sign.
- Identifying the Correct Method
To solve for \(d\) in the inequality \(4d > 24\), we need to divide both sides by the coefficient of \(d\), which is 4. Multiplying, adding, or subtracting 4 would not result in an isolated \(d\). Therefore, the correct method to solve this inequality is to divide both sides by 4.
- Solving the Inequality
We apply the chosen method:
\[\frac{4d}{4} > \frac{24}{4}\]
Simplifying both sides, we get:
\[d > 6\]
This inequality represents all values of \(d\) that are greater than 6.
- Conclusion
The method to solve \(4d > 24\) is to divide both sides by 4. Following this method, we find the solution is \(d > 6\). The final answer is \(\boxed{d > 6}\).
Examples
Suppose you are managing a small business and you have a budget of \(\$24\) for purchasing notebooks. If each notebook costs \(\$4\), you want to find out how many notebooks you can buy. Since you want to spend more than \(\$24\) (perhaps you are considering bulk discounts or other factors), the inequality \(4d > 24\) represents the number of notebooks \(d\) you would need to purchase to exceed that budget. Dividing both sides by 4 shows that you need to buy more than 6 notebooks to spend over \(\$24\).