What minus 23 equals 17
The Correct Answer and Explanation is :
To solve the equation ( x – 23 = 17 ), we need to isolate ( x ). The goal is to determine what value of ( x ) when subtracted by 23 gives us 17.
Step 1: Add 23 to both sides.
We can start solving the equation by adding 23 to both sides. This step helps to move the -23 away from ( x ).
[
x – 23 + 23 = 17 + 23
]
This simplifies to:
[
x = 40
]
Step 2: Verification.
To ensure our solution is correct, we can verify it by substituting ( x = 40 ) back into the original equation:
[
40 – 23 = 17
]
Calculating the left side:
[
40 – 23 = 17
]
Since both sides of the equation are equal, our solution is verified.
Explanation of the Process:
In solving equations like this one, the goal is to isolate the variable (in this case, ( x )). The operation performed on one side of the equation must also be performed on the other side to maintain equality. This is a fundamental property of algebra, known as the “balance” principle, where whatever you do to one side of the equation, you must also do to the other side.
This approach can be applied to more complex equations as well, emphasizing the importance of maintaining the equality while isolating the variable.
Understanding how to manipulate equations is a critical skill in algebra, as it lays the groundwork for more advanced topics in mathematics, such as functions, graphs, and calculus. By practicing these techniques, one becomes more comfortable with handling various types of equations and enhances their problem-solving abilities.