Solve $3 k x+24=9 k x$ for $x$.
A. $x=\frac{4}{k}$
B. $x=-\frac{4}{k}$
C. $x=\frac{2}{k}$
D. $x=-\frac{2}{k}$
Answer (1)
Subtract 3 k x from both sides: 24 = 6 k x .
Divide both sides by 6 k : x = 6 k 24 .
Simplify the fraction: x = k 4 .
The solution is x = k 4 .
Explanation
Understanding the Problem We are given the equation 3 k x + 24 = 9 k x and we want to solve for x .
Isolating x terms First, we want to isolate the terms with x on one side of the equation. To do this, we subtract 3 k x from both sides of the equation: 3 k x + 24 − 3 k x = 9 k x − 3 k x 24 = 6 k x
Isolating x Now, we want to isolate x . To do this, we divide both sides of the equation by 6 k :
6 k 24 = 6 k 6 k x x = 6 k 24
Simplifying the fraction Finally, we simplify the fraction: x = k 4
Finding the correct option Comparing our solution x = k 4 with the given options, we see that it matches option A.
Examples
This problem demonstrates how to solve a linear equation for a specific variable. In real life, this skill can be used to solve for unknown quantities in various scenarios, such as determining the required amount of ingredients in a recipe based on the desired yield, or calculating the distance traveled given the speed and time.
