$6 k+10.5=3 k+12$
$k=$ ?
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 equation 6 k + 10.5 = 3 k + 12 and asked to solve for k . We will isolate k by performing algebraic manipulations on both sides of the equation.
Isolating k terms First, subtract 3 k from both sides of the equation to get the terms with k on one side:
6 k + 10.5 − 3 k = 3 k + 12 − 3 k
This simplifies to:
3 k + 10.5 = 12
Isolating the k term Next, subtract 10.5 from both sides of the equation to isolate the term with k :
3 k + 10.5 − 10.5 = 12 − 10.5
This simplifies to:
3 k = 1.5
Solving for k Finally, divide both sides of the equation by 3 to solve for k :
3 3 k = 3 1.5
This simplifies to:
k = 0.5
Final Answer Therefore, the solution to the equation 6 k + 10.5 = 3 k + 12 is k = 0.5 .
Examples
Understanding linear equations is crucial in many real-world scenarios. For instance, imagine you are running a small business and want to calculate your profit. If your total revenue is represented by 6 k + 10.5 and your total cost is 3 k + 12 , where k is the number of units you sell, solving the equation 6 k + 10.5 = 3 k + 12 helps you determine the break-even point—the number of units you need to sell to cover your costs. In this case, you would need to sell 0.5 units to break even. This concept extends to more complex financial analyses, resource allocation, and strategic planning.
