Solve $5 x-c=k$ for $x$.
A. $x=\frac{k-c}{5}$
B. $x=\frac{k+c}{5}$
C. $x=5(k-c)$
D. $x=5(k+c)$
Answer (1)
Add c to both sides of the equation: 5 x = k + c .
Divide both sides by 5 to isolate x : x = 5 k + c .
The solution for x is 5 k + c .
The correct answer is B: x = 5 k + c
Explanation
Understanding the Problem We are given the equation 5 x − c = k and we want to solve for x . This means we want to isolate x on one side of the equation.
Isolating the x term First, we add c to both sides of the equation to get rid of the − c term on the left side:
5 x − c + c = k + c
This simplifies to:
5 x = k + c
Solving for x Next, we divide both sides of the equation by 5 to isolate x :
5 5 x = 5 k + c
This simplifies to:
x = 5 k + c
Final Answer Therefore, the solution for x is 5 k + c . Looking at the multiple choice options, we see that this corresponds to option B.
Examples
Solving for a variable is a fundamental skill in algebra and is used in many real-world applications. For example, imagine you are buying concert tickets online. The total cost, k , is calculated as 5 times the number of tickets, x , plus a service fee, c . If you know the total cost, k , and the service fee, c , you can solve for x to determine how many tickets you can buy. The equation 5 x − c = k models this situation, where x represents the number of tickets, c is the service fee, and k is the total cost. Solving for x gives you x = 5 k + c , which tells you the number of tickets you can purchase given the total cost and service fee.
