- Identify the equation: \(v - 9.38 = 3.2\).
- Add 9.38 to both sides to isolate the variable: \(v = 3.2 + 9.38\).
- Calculate the sum of the two numbers: \(v = 12.58\).
- State the final answer: \(\boxed{12.58}\).
Explanation
- Analysis of the Problem
We are given the linear equation \(v - 9.38 = 3.2\). Our objective is to determine the value of the variable \(v\). This is a simple algebraic equation where we need to isolate the variable by removing the constant term associated with it.
- Isolating the Variable v
To isolate \(v\), we perform the inverse operation of subtracting \(9.38\), which is adding \(9.38\) to both sides of the equation:
\[v - 9.38 + 9.38 = 3.2 + 9.38\]
This simplifies to:
\[v = 3.2 + 9.38\]
- Calculating the Final Value
Now, perform the addition of the decimal numbers:
\[v = 12.58\]
Thus, the value of \(v\) is \(12.58\).
Examples
In many real-world scenarios, we encounter situations where a starting value has been reduced by a specific amount, and we need to determine the original value. For example, if you are tracking your bank balance and you know that after withdrawing \(\$9.38\), your remaining balance is \(\$3.20\), you can use this equation \(v - 9.38 = 3.20\) to find that your initial balance \(v\) was \(\$12.58\). This fundamental algebraic skill of balancing an equation helps in financial planning, inventory management, and various scientific measurements.