Solve for k.
6k + 10.5 = 3k + 12
Answer (2)
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 solution for k . We will solve this equation step by step.
Isolating k terms First, we want to isolate the terms with k on one side of the equation. To do this, we 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 constant terms Next, we want to isolate the constant terms on the other side of the equation. To do this, we subtract 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, to solve for k , we divide both sides of the equation by 3 :
3 3 k = 3 1.5 This gives us: k = 0.5
Final Answer Therefore, the solution to the linear equation 6 k + 10.5 = 3 k + 12 is k = 0.5 .
Examples
Linear equations are used in many real-world applications, such as calculating the cost of items, determining the speed of an object, or predicting the growth of a population. For example, if you know the cost of a certain number of items and you want to find the cost of a different number of items, you can use a linear equation to solve the problem. Understanding how to solve linear equations is a fundamental skill in mathematics and is essential for solving many practical problems.
To solve the equation 6 k + 10.5 = 3 k + 12 , we first isolate the terms involving k and the constants. After simplifying the equation step-by-step, we find that k = 0.5 .
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