Solve $k x+7=4$ for $x$.
A. $x=\frac{k}{3}$
B. $x=-\frac{k}{3}$
C. $x=\frac{3}{k}$
D. $x=-\frac{3}{k}$
Answer (1)
Subtract 7 from both sides: k x = 4 − 7 = − 3 .
Divide both sides by k : x = k − 3 .
Simplify: x = − k 3 .
The solution is − k 3 .
Explanation
Understanding the Problem We are given the equation k x + 7 = 4 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 7 from both sides of the equation to isolate the term with x :
k x + 7 − 7 = 4 − 7
Simplifying the Equation Simplifying the right side, we have: k x = − 3
Solving for x Now, we divide both sides by k to solve for x :
x = k − 3
Final Answer Therefore, the solution is x = − k 3 .
Examples
Imagine you are trying to determine how much of a certain ingredient to add to a recipe. If k represents the amount of an ingredient you add per unit and x is the number of units, and you know that k x + 7 = 4 represents the total 'effect' you want to achieve (where 7 is a base effect and 4 is the target effect), solving for x tells you how many units you need to use to reach your target effect. For example, if k = 2 , then x = − 2 3 , meaning you would need to reduce the ingredient to achieve the desired effect.
