Solve x + 9 = 18 – 2x
The Correct Answer and Explanation is :
To solve the equation ( x + 9 = 18 – 2x ), we need to isolate the variable ( x ). Here’s how to do it step by step:
- Start with the original equation:
[
x + 9 = 18 – 2x
] - Add ( 2x ) to both sides to get all ( x ) terms on one side of the equation:
[
x + 2x + 9 = 18
]
This simplifies to:
[
3x + 9 = 18
] - Next, subtract 9 from both sides to isolate the ( 3x ) term:
[
3x + 9 – 9 = 18 – 9
]
Simplifying this gives:
[
3x = 9
] - Now, divide both sides by 3 to solve for ( x ):
[
\frac{3x}{3} = \frac{9}{3}
]
Therefore, we find:
[
x = 3
]
Thus, the solution to the equation ( x + 9 = 18 – 2x ) is ( x = 3 ).
Explanation
This equation involves balancing both sides by performing equivalent operations. We start by recognizing that the goal is to isolate ( x ). This is a fundamental skill in algebra, known as solving linear equations. The first step was to combine like terms by moving ( -2x ) to the left side. This step is crucial because it simplifies our equation, allowing us to focus on isolating ( x ).
Next, we eliminated the constant term on the left side by subtracting 9 from both sides. This reinforces the principle that whatever we do to one side of the equation, we must do to the other to maintain equality. Finally, dividing by 3 allows us to solve for ( x ).
In summary, the key steps of rearranging, simplifying, and performing arithmetic operations are essential in finding the value of ( x ). These principles form the basis of algebra and are applicable in various fields, including science, engineering, and finance, where problem-solving is required.