Solve $4 k x+10 k x=7$ for $x$
A. $x=\frac{1}{2 k}$
B. $x=2 k$
C. $x=\frac{k}{2}$
D. $x=\frac{2}{k}$
Answer (1)
Combine like terms: 4 k x + 10 k x = 14 k x .
Rewrite the equation: 14 k x = 7 .
Divide both sides by 14 k : x = 14 k 7 .
Simplify the fraction: x = 2 k 1 .
Explanation
Problem Setup We are given the equation 4 k x + 10 k x = 7 and we want to solve for x .
Combining Like Terms First, we combine the like terms on the left side of the equation: 4 k x + 10 k x = ( 4 k + 10 k ) x = 14 k x So the equation becomes 14 k x = 7 .
Isolating x Next, we want to isolate x . To do this, we divide both sides of the equation by 14 k : 14 k 14 k x = 14 k 7 This simplifies to x = 14 k 7
Simplifying the Fraction Finally, we simplify the fraction: x = 14 k 7 = 2 k 1 So the solution is x = 2 k 1 .
Final Answer Therefore, the solution for x is 2 k 1 .
Examples
Imagine you are distributing flyers for a local event. You know that you need to cover 7 blocks and that each person can cover 14 k blocks per hour, where k is a constant representing their walking speed and efficiency. The equation 14 k x = 7 helps you determine how many hours ( x ) it will take one person to cover all the blocks. Solving for x gives you x = 2 k 1 , which tells you the time required in terms of the constant k . If k = 1 , it takes 0.5 hours. If k = 2 , it takes 0.25 hours.
