Solve $6 x-17=k$ for $x$.
A. $x=\frac{k+17}{6}$
B. $x=6 k+102$
C. $x=k+11$
D. $x=\frac{k}{6}+17$
Answer (1)
Add 17 to both sides of the equation: 6 x = k + 17 .
Divide both sides by 6: x = 6 k + 17 .
The solution for x is 6 k + 17 .
The correct answer is: x = 6 k + 17
Explanation
Understanding the Problem We are given the equation 6 x − 17 = k and we want to solve for x . This means we want to isolate x on one side of the equation.
Isolating the Term with x First, we add 17 to both sides of the equation to get rid of the -17 on the left side: 6 x − 17 + 17 = k + 17 6 x = k + 17
Solving for x Next, we divide both sides of the equation by 6 to isolate x :
6 6 x = 6 k + 17 x = 6 k + 17
Final Answer Therefore, the solution for x is x = 6 k + 17 . Comparing this to the given options, we see that it matches option A.
Examples
In physics, this type of equation can be used to relate force and acceleration. If you have a scenario where the net force on an object ( 6 x ) minus a constant force (17 Newtons) equals another force ( k ), you can solve for x to find the acceleration of the object. For instance, if k represents the net force and x represents the acceleration, the equation 6 x − 17 = k helps determine the acceleration needed to achieve a certain net force, considering other forces acting on the object.
