Solve $5 x+14=k$ for $x$.
A. $x=5 k-14$
B. $x=k-14$
C. $x=\frac{k+14}{5}$
D. $x=\frac{k-14}{5}$

Subtract 14 from both sides of the equation: 5 x = k − 14 .
Divide both sides by 5 to isolate x : x = 5 k − 14 ​ .
The solution for x is 5 k − 14 ​ ​ .

Explanation

Isolating x We are given the equation 5 x + 14 = k and we want to solve for x . This means we want to isolate x on one side of the equation.

Subtracting 14 First, we subtract 14 from both sides of the equation to get rid of the constant term on the side with x :
5 x + 14 − 14 = k − 14 5 x = k − 14

Dividing by 5 Next, we divide both sides of the equation by 5 to isolate x :
5 5 x ​ = 5 k − 14 ​ x = 5 k − 14 ​

Final Answer Therefore, the solution for x is x = 5 k − 14 ​ . Comparing this to the given options, we see that it matches option D.


Examples
In physics, this type of equation can represent a simple linear relationship between variables. For example, if x represents the temperature in Celsius and k represents the temperature in Fahrenheit, the equation 5 x + 14 = k (after adjusting constants) could relate the two scales. Solving for x allows you to convert Fahrenheit to Celsius. Understanding how to manipulate and solve such equations is crucial for making conversions and understanding relationships between different physical quantities.

Answered by GinnyAnswer | 2025-07-04