- Analyze the linear equation \(j + 54 = 86\).
- Isolate the variable \(j\) by subtracting 54 from both sides.
- Calculate the result: \(86 - 54 = 32\).
- The final value is \(\boxed{32}\).
Explanation
- Analysis of the Equation
The equation given is \(j + 54 = 86\). Our goal is to isolate the variable \(j\). This is a linear equation where we need to determine the value that, when added to 54, results in 86.
- Solving for \(j\)
To isolate \(j\), we subtract 54 from both sides of the equation using the property of equality:
\[j + 54 - 54 = 86 - 54\]
This simplifies to:
\[j = 86 - 54\]
Now, perform the subtraction:
\[86 - 54 = 32\]
Thus, the value of \(j\) is 32.
Examples
In everyday life, simple linear equations are everywhere. For example, if you have a budget of \$86 for a project and you have already spent \$54 on materials, you can find the remaining amount \(j\) you have left for other supplies by solving \(j + 54 = 86\). By subtracting the spent amount from your total budget, you determine that you have \(\$32\) remaining. This foundational skill allows for efficient personal finance management and resource allocation.