Solve the equation.
$y+3=-y+9$
A. $y=1$
B. $y=3$
C. $y=6$
D. $y=9$
Answer (1)
Add y to both sides: 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 will use algebraic manipulation to isolate y on one side of the equation.
Adding y to Both Sides First, add y to both sides of the equation to get all the y terms on one side: y + 3 + y = − y + 9 + y This simplifies to: 2 y + 3 = 9
Subtracting 3 from Both Sides Next, subtract 3 from both sides of the equation to isolate the term with y :
2 y + 3 − 3 = 9 − 3 This simplifies to: 2 y = 6
Dividing by 2 Finally, divide both sides of the equation by 2 to solve for y :
2 2 y = 2 6 This simplifies to: y = 3
Final Answer Therefore, the solution to the equation y + 3 = − y + 9 is y = 3 .
Examples
In real life, solving linear equations like this can help you determine how much of something you need to add or subtract to balance a situation. For example, if you're managing a budget and need to figure out how much to save each month to reach a specific goal, you might use a similar equation to calculate the required savings amount. Understanding how to manipulate equations allows you to solve for unknown variables and make informed decisions in various practical scenarios.
