Question

what is the solution to the linear equation?
6k + 10.5 = 3k + 12
\\( k = 0.5 \\)
\\( k = 2 \\)
\\( k = 7.3 \\)
\\( k = 9 \\)

Explanation:

Step1: Subtract \(3k\) from both sides

To isolate the variable terms on one side, we subtract \(3k\) from both sides of the equation \(6k + 10.5 = 3k + 12\). This gives us \(6k - 3k + 10.5 = 3k - 3k + 12\), which simplifies to \(3k + 10.5 = 12\).

Step2: Subtract \(10.5\) from both sides

Next, we subtract \(10.5\) from both sides to isolate the term with the variable. So, \(3k + 10.5 - 10.5 = 12 - 10.5\), which simplifies to \(3k = 1.5\).

Step3: Divide both sides by 3

To solve for \(k\), we divide both sides of the equation \(3k = 1.5\) by 3. This gives us \(\frac{3k}{3}=\frac{1.5}{3}\), so \(k = 0.5\).

Answer:

\(k = 0.5\) (corresponding to the option: \(k = 0.5\))