Verified Answer :

  • Identify the given equation: \(3u = 66\).
  • Divide both sides of the equation by 3 to isolate \(u\): \(u = \frac{66}{3}\).
  • Calculate the result: \(u = 22\).
  • The final value is \(\boxed{22}\).

Explanation

  1. Problem Analysis

We are given the linear equation \(3u = 66\). Our goal is to isolate the variable \(u\) to find its value. This is a standard algebraic problem where we need to solve for an unknown variable by performing inverse operations.

  1. Solving for u

To isolate \(u\), we need to eliminate the coefficient 3 from the left-hand side of the equation. Since \(u\) is multiplied by 3, we perform the inverse operation, which is division, on both sides of the equation:
\[u = \frac{66}{3}\]
Performing the division, we get:
\[u = 22\]

  1. Verification and Conclusion

We have found the value of \(u\). To verify, we can substitute \(u = 22\) back into the original equation:
\[3 \times 22 = 66\]
The equation holds true, so our solution is correct. Thus, the final value is \(\boxed{22}\).

Examples

Solving linear equations is essential in real-life scenarios, such as budgeting. Suppose you are buying 3 identical notebooks for a total of \$66. To find the cost of a single notebook, you divide the total cost by the number of notebooks: \(3u = 66\), where \(u\) is the price per notebook. By solving for \(u\), you determine that each notebook costs \(\$22\). This skill allows you to calculate unit prices and manage expenses effectively.

Related Questions