Solve each equation for the indicated variable. Round answers to two decimal places as necessary.
$\frac{C}{-10}-3=12$
Answer (1)
Add 3 to both sides of the equation: − 10 C = 15 .
Multiply both sides by -10: C = 15 × − 10 .
Calculate the value of C: C = − 150 .
The solution is: − 150 .
Explanation
Problem Analysis We are given the equation − 10 C − 3 = 12 and we want to solve for C .
Isolating the Term with C First, we need to isolate the term containing C . To do this, we add 3 to both sides of the equation: − 10 C − 3 + 3 = 12 + 3 − 10 C = 15
Solving for C Now, to solve for C , we multiply both sides of the equation by -10: ( − 10 C ) × ( − 10 ) = 15 × ( − 10 ) C = − 150
Final Answer Since the result is an integer, no rounding is necessary.
Examples
Imagine you are managing a budget. If a certain expense, when divided by -10 and then reduced by 3, results in a total of 12, this equation helps you determine the original amount of that expense. Understanding how to solve for variables in equations like this is crucial for financial planning and tracking expenses accurately. For example, if − 10 C − 3 = 12 represents a simplified model of your budget, solving for C tells you the initial value before the division and subtraction.
