Which equation is equivalent to x+15=36 ?
A. x=3
B. x+15=9
C. x+15=−6
D. x=24
The Correct Answer and Explanation is:
To solve the equation ( x + 15 = 36 ), we need to isolate the variable ( x ). The goal is to determine the value of ( x ) that makes the equation true.
Steps to Solve the Equation:
- Start with the original equation:
[
x + 15 = 36
] - Subtract 15 from both sides:
To isolate ( x ), we can perform the operation of subtraction. This involves taking away 15 from both sides of the equation, which keeps the equation balanced.
[
x + 15 – 15 = 36 – 15
] - Simplify both sides:
After subtracting 15 from the left side, it simplifies to ( x ):
[
x = 36 – 15
]
On the right side, performing the subtraction gives:
[
x = 21
]
Understanding the Equivalent Equations:
To find an equation that is equivalent to the original equation, we can transform the original equation into different forms. An equivalent equation is one that has the same solution.
Among the answer choices provided:
- A. ( x = 3 ) is incorrect since we found ( x = 21 ).
- B. ( x + 15 = 9 ) can be tested: If we rearrange it to solve for ( x ), we subtract 15 from both sides to get ( x = 9 – 15 ), leading to ( x = -6 ). This does not match our solution.
- C. ( x + 15 = -6 ) can also be checked: Rearranging gives ( x = -6 – 15 ), resulting in ( x = -21 ), which is not correct.
- D. ( x = 24 ) is also not correct since we found ( x = 21 ).
To verify, we should check the original equation with the correct solution. We originally calculated that:
[
x + 15 = 36
]
Setting ( x = 21 ) gives us:
[
21 + 15 = 36
]
Since this is true, the value of ( x ) we found is correct.
Conclusion:
None of the provided options are equivalent to the equation ( x + 15 = 36 ). The correct value of ( x ) that satisfies the equation is ( x = 21 ). The process of isolating the variable and verifying through substitution is crucial in solving equations effectively.