What is the solution to the linear equation?
$6 k+10.5=3 k+12$
A. $k=0.5$
B. $k=2$
C. $k=7.3$
D. $k=9$
Answer (1)
Subtract 3 k from both sides: 3 k + 10.5 = 12 .
Subtract 10.5 from both sides: 3 k = 1.5 .
Divide both sides by 3 : k = 0.5 .
The solution to the equation is 0.5 .
Explanation
Problem Analysis We are given the linear equation 6 k + 10.5 = 3 k + 12 and asked to find the value of k that satisfies the equation.
Isolating k terms To solve for k , we first want to isolate the terms with k on one side of the equation. We can subtract 3 k from both sides of the equation: 6 k + 10.5 − 3 k = 3 k + 12 − 3 k This simplifies to: 3 k + 10.5 = 12
Isolating k Next, we want to isolate the k term by subtracting 10.5 from both sides of the equation: 3 k + 10.5 − 10.5 = 12 − 10.5 This simplifies to: 3 k = 1.5
Solving for k Finally, we divide both sides of the equation by 3 to solve for k :
3 3 k = 3 1.5 k = 0.5
Final Answer Therefore, the solution to the linear equation is k = 0.5 .
Examples
Linear equations are used in everyday life to calculate costs, distances, and other quantities. For example, if you want to buy a certain number of items at a store, and each item costs a fixed amount, you can use a linear equation to calculate the total cost. Suppose you want to buy movie tickets that cost $7.5 each, and you have a coupon for 2 o ff t h ee n t i re p u rc ha se . T h ee q u a t i o n t oc a l c u l a t e t h e t o t a l cos t C f or n t i c k e t s i s C = 7.5n - 2$. If you have $35 to spend, you can solve the equation 35 = 7.5 n − 2 to find out how many tickets you can buy. Adding 2 to both sides gives 37 = 7.5 n , and dividing by 7.5 gives n = 4.93 . Since you can't buy a fraction of a ticket, you can buy 4 tickets.
