- Substitute the value \(x = 34.5\) into the expression \(\frac{x}{6}\).
- Calculate the resulting value of the expression, which is \(5.75\).
- Compare this result to the right-hand side of the equation, which is also \(5.75\).
- Conclude that since both sides are equal, the value is a solution: \(\boxed{\text{Yes}}\).
Explanation
- Problem Analysis
To determine if \(x = 34.5\) is a solution to the equation \(\frac{x}{6} = 5.75\), we substitute the given value of \(x\) into the left-hand side of the equation and compare it to the right-hand side. The equation is \(\frac{x}{6} = 5.75\), so the left-hand side is \(\frac{x}{6}\) and the right-hand side is \(5.75\).
- Testing the Proposed Solution
We substitute \(x = 34.5\) into the left-hand side of the equation:
\[\frac{34.5}{6}.\]
Performing the division, we find that:
\[\frac{34.5}{6} = 5.75.\]
- Conclusion
We compare the result of our calculation to the right-hand side of the equation:
\[5.75 = 5.75.\]
Since the value of the left-hand side is equal to the value of the right-hand side, the proposed value \(x = 34.5\) is indeed a solution to the equation \(\frac{x}{6} = 5.75\). The final answer is Yes. \(\boxed{\text{Yes}}\)
Examples
In many real-life situations, we need to verify if a proposed value works for a given constraint. For instance, if you are planning to share a budget of \(\$5.75\) equally among 6 people, you might ask if a total amount of \(\$34.50\) is the correct total needed. By checking if \(\frac{34.50}{6} = 5.75\), you confirm your calculations are correct and that the total amount is sufficient to meet your goal. This simple process of substitution is a fundamental skill in solving problems involving proportions and budgeting.