What equation can be used to find the value of x
The Correct Answer and Explanation is :
To find the value of ( x ) in an equation, we often use algebraic equations, where the form of the equation dictates the approach taken. A common equation to illustrate this is a linear equation, such as:
[
ax + b = c
]
where:
- ( a ), ( b ), and ( c ) are constants.
- ( x ) is the variable we want to solve for.
Steps to Solve for ( x )
- Isolate the term with ( x ): Begin by moving the constant ( b ) to the other side of the equation. This can be achieved by subtracting ( b ) from both sides: [
ax = c – b
] - Solve for ( x ): Next, divide both sides of the equation by ( a ) (assuming ( a \neq 0 )) to isolate ( x ): [
x = \frac{c – b}{a}
]
Example
Let’s say we have the equation:
[
3x + 6 = 15
]
- First, isolate the term with ( x ): [
3x = 15 – 6
]
[
3x = 9
] - Next, solve for ( x ) by dividing both sides by 3: [
x = \frac{9}{3} = 3
]
Explanation
In the example, we start with a linear equation that has a variable ( x ) multiplied by a constant (3) and a constant (6) added to it. The objective is to find the value of ( x ) that makes the equation true. By following the steps to isolate ( x ), we manipulate the equation using basic arithmetic operations, ensuring that whatever operation we perform on one side, we do the same on the other side to maintain the equality. This method is fundamental in algebra and can be applied to more complex equations, including quadratic equations and systems of equations, by employing similar isolation techniques and advanced methods as needed.