- To solve the equation \(2v = -80\), isolate the variable \(v\) by dividing both sides of the equation by 2.
- Perform the calculation \(\frac{-80}{2}\) to find the value of \(v\).
- The result is \(v = \boxed{-40}\).
Explanation
- Understanding the Equation
The objective is to solve the linear equation \(2v = -80\) for the variable \(v\). This is a basic algebraic equation where the variable is multiplied by a coefficient. To isolate \(v\), we need to perform the inverse operation of multiplication, which is division.
- Solving for v
To isolate \(v\), divide both sides of the equation by the coefficient of \(v\), which is 2:
\[\frac{2v}{2} = \frac{-80}{2}\]
Calculating the right side:
\[v = -40\]
This gives us the value of \(v\).
Examples
In everyday life, simple linear equations like this appear when managing budgets. For example, if you spend a total of \$80 on 2 identical items, the cost of one item \(v\) is found by dividing the total cost by the number of items: \(\$80 / 2 = \$40\), so the cost per item is \(\$40\). Understanding how to isolate a variable helps in solving many real-world problems involving rates, costs, and measurements.