Select the correct answer.

Which equation is correctly rewritten to solve for $x$?
$-f x-g=h$
A. $x=\frac{g-h}{-f}$
B. $x=\frac{h+g}{-f}$
C. $x=\frac{h-g}{-f}$
D. $x=\frac{h+g}{f}$

Add g to both sides of the equation: − f x = h + g .
Divide both sides by − f : x = − f h + g ​ .
The correct expression for x is − f h + g ​ .
Therefore, the answer is x = − f h + g ​ ​ .

Explanation

Understanding the Problem We are given the equation − f x − g = h and asked to solve for x . This involves isolating x on one side of the equation.

Isolating the x term First, we add g to both sides of the equation to isolate the term with x : − f x − g + g = h + g − f x = h + g

Solving for x Next, we divide both sides by − f to solve for x : − f − f x ​ = − f h + g ​ x = − f h + g ​

Identifying the Correct Option Comparing our result with the given options, we find that option B matches our solution: x = − f h + g ​ .


Examples
In physics, this type of equation can represent a force balance where you need to solve for an unknown variable, such as the position of an object under certain forces. For example, if − f x − g = h represents the net force acting on an object, where f is a constant related to friction, x is the object's position, g is the gravitational force, and h is an external force, solving for x tells you the object's position given the forces acting on it. Understanding how to isolate and solve for variables is crucial in many scientific and engineering applications.

Answered by GinnyAnswer | 2025-07-04

To solve the equation − f x − g = h for x , we first add g to both sides, yielding − f x = h + g . Then, dividing both sides by − f gives us x = − f h + g ​ . Thus, the correct answer is option B.
;

Answered by Anonymous | 2025-07-06