Question

linear equations and inequalities
what is the solution to the linear equation?
$6k + 10.5 = 3k + 12$
$k = 9$
$k = 7.3$
$k = 2$
$k = 0.5$

Explanation:

Step1: Subtract 3k from both sides

To isolate the variable terms, we subtract \(3k\) from each side 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 \(3\). That is, \(\frac{3k}{3}=\frac{1.5}{3}\), which gives \(k = 0.5\).

Answer:

\(k = 0.5\)