Solve $6 x+c=k$ for $x$.
A. $x=\frac{k+c}{6}$
B. $x=6(k-c)$
C. $x=\frac{k-c}{6}$
D. $x=6(k+c)$
Answer (1)
Subtract c from both sides of the equation: 6 x = k − c .
Divide both sides by 6 to isolate x : x = 6 k − c .
The solution is x = 6 k − c .
Therefore, the correct option is C: x = 6 k − c .
Explanation
Understanding the Problem We are given the equation 6 x + c = k and asked to solve for x . This means we want to isolate x on one side of the equation.
Isolating the Term with x First, we subtract c from both sides of the equation to get: 6 x + c − c = k − c 6 x = k − c
Solving for x Next, we divide both sides of the equation by 6 to isolate x : 6 6 x = 6 k − c x = 6 k − c
Identifying the Correct Option Comparing our solution x = 6 k − c with the given options, we see that it matches option C.
Examples
In physics, this type of equation can represent a simplified model of force equilibrium. For example, if 6 x represents the force exerted by a spring, c is a constant force acting against it, and k is the total force required for equilibrium, solving for x tells us how much the spring needs to be stretched or compressed to maintain that equilibrium. Understanding how to isolate variables in such equations is crucial for predicting and controlling physical systems.
