- The problem is a linear equation in the form \(b - 644 = -27\).
- To isolate \(b\), add 644 to both sides of the equation.
- Calculating the sum gives \(b = 644 - 27 = 617\).
- The final value is \(\boxed{617}\).
Explanation
- Problem Analysis and Objective
The problem asks to solve for the variable \(b\) in the linear equation \(b - 644 = -27\). Our goal is to isolate \(b\) to determine its numerical value. This is a standard algebraic equation where the operation of subtraction is present, and we can solve it by performing the inverse operation, which is addition.
- Solving the Equation
To isolate \(b\), we need to add 644 to both sides of the equation:
\[b - 644 + 644 = -27 + 644\]
By simplifying the left side, we get \(b\). On the right side, we perform the arithmetic: \(644 - 27 = 617\). Therefore, \(b = 617\).
Examples
In real life, this type of equation appears when tracking balances. For example, if your bank account balance \(b\) was reduced by a fee of \(\$644\) and you are left with a deficit of \(\$27\), you can find your original balance by solving \(b - 644 = -27\). This simple algebraic manipulation allows you to recover missing information by reversing transactions.