Solve [tex]3 k x+24=9 k x[/tex] for [tex]x[/tex].
A. [tex]x=\frac{4}{k}[/tex]
B. [tex]x=-\frac{2}{k}[/tex]
C. [tex]x=-\frac{4}{k}[/tex]
D. [tex]x=\frac{2}{k}[/tex]
Answer (1)
Subtract 3 k x from both sides: 24 = 6 k x .
Divide both sides by 6 k : x = 6 k 24 .
Simplify the fraction: x = k 4 .
The solution is x = k 4 .
Explanation
Understanding the Problem We are given the equation 3 k x + 24 = 9 k x and asked to solve for x . This means we want to isolate x on one side of the equation.
Isolating the x term First, subtract 3 k x from both sides of the equation to get all terms involving x on one side:
3 k x + 24 − 3 k x = 9 k x − 3 k x
This simplifies to:
24 = 6 k x
Isolating x Next, divide both sides of the equation by 6 k to isolate x :
6 k 24 = 6 k 6 k x
This simplifies to:
x = 6 k 24
Simplifying the fraction Finally, simplify the fraction:
x = k 4
Final Answer Therefore, the solution is x = k 4 . Looking at the multiple choice options, we see that this corresponds to option A.
Examples
In physics, this type of equation might arise when analyzing forces or motion where x represents a displacement and k is a constant related to the force. For example, if you have a scenario where the force is proportional to the displacement, solving for x helps determine the exact displacement needed to balance the forces. Understanding how to solve such equations is crucial in many engineering and physics applications, such as designing structures or analyzing mechanical systems. The ability to manipulate and solve linear equations is a fundamental skill in these fields.
