- Start with the equation \(3c - 15 = -45\).
- Add 15 to both sides to get \(3c = -30\).
- Divide both sides by 3 to isolate \(c\).
- The final solution is \(c = \boxed{-10}\).
Explanation
- Analyzing the Equation
The given equation is \(3c - 15 = -45\). This is a linear equation in one variable, \(c\). Our goal is to isolate \(c\) to find its value. To do this, we need to perform algebraic operations on both sides of the equation to maintain equality.
- Isolating the Term with \(c\)
To isolate the term with \(c\), we start by adding \(15\) to both sides of the equation:
\[3c - 15 + 15 = -45 + 15\]
This simplifies the equation to:
\[3c = -30\]
- Solving for \(c\)
Now, we solve for \(c\) by dividing both sides of the equation by the coefficient of \(c\), which is \(3\):
\[\frac{3c}{3} = \frac{-30}{3}\]
Performing the division, we get:
\[c = -10\]
Examples
Linear equations appear frequently in everyday life, for example, when calculating how long it will take to pay off a debt. If you owe \$45 and you have already paid off \$15 by making a small initial payment, you can represent the remaining amount to pay in installments (let's say 3 equal installments of \(c\) dollars each) as \(3c - 15 = -45\). Solving this equation tells you how much each installment should be. In this case, solving it helps manage your finances effectively by knowing exactly how much you need to contribute.