Solve for $y: -5y + 6 = 16$
Answer (1)
Subtract 6 from both sides: − 5 y = 10 .
Divide both sides by -5: y = − 5 10 .
Simplify to find the value of y .
The solution is: − 2 .
Explanation
Understanding the Problem We are given the equation − 5 y + 6 = 16 and we want to solve for y . This means we want to isolate y on one side of the equation.
Subtracting 6 from both sides First, we subtract 6 from both sides of the equation to get rid of the constant term on the left side: − 5 y + 6 − 6 = 16 − 6
Simplifying the equation This simplifies to: − 5 y = 10
Dividing by -5 Next, we divide both sides of the equation by -5 to isolate y :
− 5 − 5 y = − 5 10
Finding the value of y This simplifies to: y = − 2
Final Answer Therefore, the solution to the equation − 5 y + 6 = 16 is y = − 2 .
Examples
Imagine you are managing a small business and you need to calculate the break-even point for a product. The equation − 5 y + 6 = 16 could represent a simplified model where y is the number of units you need to sell, 6 represents your fixed costs, and 16 represents the total revenue needed to cover costs and achieve a certain profit target. Solving for y tells you exactly how many units you need to sell to meet that target. Understanding how to solve such equations is crucial for making informed business decisions and managing finances effectively. This algebraic approach helps in determining the required sales volume to achieve financial goals.
