Solve $30 k x-6 k x=8$ for $x$.
A. $x=3 k$
B. $x=\frac{3}{x}$
C. $x=\frac{1}{3 k}$
D. $x=\frac{k}{3}
Answer (2)
Combine like terms: 30 k x − 6 k x = 24 k x .
Rewrite the equation: 24 k x = 8 .
Divide both sides by 24 k : x = 24 k 8 .
Simplify the fraction: x = 3 k 1 .
The solution is x = 3 k 1 .
Explanation
Understanding the Problem We are given the equation 30 k x − 6 k x = 8 and asked to solve for x . This involves simplifying the equation and isolating x on one side.
Combining Like Terms First, we combine the terms on the left side of the equation:
30 k x − 6 k x = ( 30 k − 6 k ) x = 24 k x
So the equation becomes:
24 k x = 8
Isolating x Next, we isolate x by dividing both sides of the equation by 24 k :
x = 24 k 8
Simplifying the Fraction Finally, we simplify the fraction:
x = 24 k 8 = 3 k 1
Thus, the solution is x = 3 k 1 .
Final Answer Therefore, the solution to the equation 30 k x − 6 k x = 8 for x is x = 3 k 1 .
Examples
In physics, this type of equation might arise when calculating the position of an object moving with constant velocity under the influence of a force. For example, if k represents a constant related to the force and x represents the position, solving for x gives the object's position at a certain time. Similarly, in electrical circuits, if you have a circuit with resistance and inductance, you might encounter an equation of this form when analyzing the current flow. Solving for x could give you the value of a component in the circuit.
By simplifying the equation 30 k x − 6 k x = 8 , we find that x = 3 k 1 . The answer corresponds to option C. This involves combining like terms, isolating x , and simplifying the resulting fraction.
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