How do I solve kx+3x=4 for x
The Correct Answer and Explanation is:
To solve the equation ( kx + 3x = 4 ) for ( x ), we will follow several steps that involve combining like terms and isolating the variable. Here’s a step-by-step breakdown of the solution:
Step 1: Combine Like Terms
The first step is to combine the terms on the left side of the equation. The equation can be rewritten as follows:
[
(k + 3)x = 4
]
In this step, we have factored out ( x ) from both ( kx ) and ( 3x ), resulting in ( (k + 3)x ).
Step 2: Isolate the Variable
Next, we want to isolate ( x ) by getting rid of the coefficient ( (k + 3) ) in front of ( x ). To do this, we divide both sides of the equation by ( (k + 3) ):
[
x = \frac{4}{k + 3}
]
Step 3: Solution
Now we have expressed ( x ) in terms of ( k ). The final solution to the equation ( kx + 3x = 4 ) is:
[
x = \frac{4}{k + 3}
]
Explanation of the Process
In solving linear equations like this one, the goal is to isolate the variable ( x ). The equation originally contained two terms with ( x ): ( kx ) and ( 3x ). By combining these terms, we simplified the equation, making it easier to handle.
Dividing by ( (k + 3) ) assumes that ( k + 3 \neq 0 ). If ( k + 3 = 0 ) (which happens when ( k = -3 )), the equation would not be valid because you cannot divide by zero. This consideration is crucial in algebraic manipulations, ensuring that solutions remain valid within defined parameters.
Overall, this method of combining like terms and isolating the variable is fundamental to solving linear equations and can be applied to various forms of similar equations. The result gives a clear expression for ( x ) in terms of ( k ), which can be useful in further applications or analyses.