Solve the equation y + 3 = -y +9
A. y = 1
B. y = 3
C. y = 6
D. y = 9H291
The Correct Answer and Explanation is:
The correct answer is B. y=3
To solve the equation ( y + 3 = -y + 9 ), we will isolate the variable ( y ) on one side of the equation.
Step-by-Step Solution:
- Start with the original equation:
[
y + 3 = -y + 9
] - Add ( y ) to both sides:
This will help eliminate ( -y ) on the right side:
[
y + y + 3 = 9
]
Simplifying gives:
[
2y + 3 = 9
] - Next, subtract 3 from both sides:
We want to isolate ( 2y ):
[
2y = 9 – 3
]
Simplifying further gives:
[
2y = 6
] - Now, divide both sides by 2:
To solve for ( y ), we divide:
[
y = \frac{6}{2}
]
Simplifying gives:
[
y = 3
]
Conclusion:
The solution to the equation ( y + 3 = -y + 9 ) is ( y = 3 ). Therefore, the correct answer is B. ( y = 3 ).
Explanation:
This equation demonstrates a simple linear relationship where ( y ) is represented on both sides. To isolate ( y ), we systematically rearranged the terms. The addition of ( y ) to both sides allowed us to consolidate all ( y ) terms on one side, forming ( 2y + 3 = 9 ). Subtracting constants from both sides is a fundamental principle in algebra that enables us to solve equations efficiently.
Linear equations like this one typically have a straightforward path to a solution due to their single-variable nature and the operations allowed in algebra. Ensuring each operation is applied equally on both sides of the equation maintains the equality, which is crucial in mathematics.
By reducing the equation step-by-step, we arrive at a clear, isolated solution for ( y ). This skill is vital for solving more complex equations encountered in algebra and beyond. Thus, being adept at manipulating equations lays the groundwork for higher-level math understanding.