- Subtract 45 from both sides to get \(\frac{c}{2} = 21\).
- Multiply both sides by 2 to solve for \(c\), resulting in \(c = 42\).
- The final value is \(\boxed{42}\).
Explanation
- Analysis of the Equation
The given equation is a linear equation in one variable:
\[\frac{c}{2} + 45 = 66\]
Our goal is to isolate the variable \(c\) to find its value. To do this, we need to perform algebraic operations on both sides of the equation while maintaining equality. The steps involved include subtraction and multiplication.
- Isolating the Variable Term
To isolate the term involving \(c\), subtract 45 from both sides of the equation:
\[\frac{c}{2} = 66 - 45\]
Performing the subtraction:
\[\frac{c}{2} = 21\]
- Solving for c
To solve for \(c\), multiply both sides of the equation by 2:
\[c = 21 \times 2\]
Performing the multiplication:
\[c = 42\]
Thus, the value of \(c\) is 42.
Examples
Imagine you are distributing a collection of items, and you start with a certain number of items divided by 2. If you add 45 more to that pile, you end up with a total of 66 items. To find out the original total number of items, you would use this algebraic process: subtracting the added items and then doubling the result to recover the original quantity. This is a common way to backtrack through a process to find the initial state.