Solve the equation
$y+3=-y+9$
Answer (1)
Add y to both sides of the equation: 2 y + 3 = 9 .
Subtract 3 from both sides: 2 y = 6 .
Divide both sides by 2: y = 3 .
The solution to the equation is 3 .
Explanation
Understanding the Problem We are given the equation y + 3 = − y + 9 and asked to solve for y . We are also given a set of possible solutions: y = 1 , y = 3 , y = 6 , y = 9 . Our goal is to find the correct value of y that satisfies the equation.
Adding y to Both Sides To solve the equation, we first want to isolate the variable y on one side of the equation. We can start by adding y to both sides of the equation: y + 3 + y = − y + 9 + y This simplifies to: 2 y + 3 = 9
Subtracting 3 from Both Sides Next, we want to isolate the term with y . We can do this by subtracting 3 from both sides of the equation: 2 y + 3 − 3 = 9 − 3 This simplifies to: 2 y = 6
Dividing by 2 Now, we want to solve for y by dividing both sides of the equation by 2: 2 2 y = 2 6 This simplifies to: y = 3
Checking the Solution Finally, we check if our solution y = 3 is among the possible solutions given. Since y = 3 is one of the possible solutions, we can conclude that the correct solution is y = 3 .
Examples
Solving linear equations like this is a fundamental skill in algebra and has many real-world applications. For example, imagine you are trying to balance a budget. You have some income, and you have some expenses. You can use a linear equation to determine how much you need to save each month to reach a specific financial goal. If y represents the amount you save each month, and the equation is y + 3 = − y + 9 , solving for y tells you the savings amount needed to balance your budget according to the given conditions.
