# How do you solve 6k + 5= 2k + 1?

Jan 8, 2018

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{5}$ and $\textcolor{b l u e}{2 k}$ from each side of the equation to isolate the $k$ term while keeping the equation balanced:

$6 k - \textcolor{b l u e}{2 k} + 5 - \textcolor{red}{5} = 2 k - \textcolor{b l u e}{2 k} + 1 - \textcolor{red}{5}$

$\left(6 - \textcolor{b l u e}{2}\right) k + 0 = 0 - 4$

$4 k = - 4$

Next, divide each side of the equation by $\textcolor{red}{4}$ to solve for $k$ while keeping the equation balanced:

$\frac{4 k}{\textcolor{red}{4}} = - \frac{4}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} k}{\cancel{\textcolor{red}{4}}} = - 1$

$k = - 1$

Jan 8, 2018

Just a simple linear equation.
$k = - 1$

#### Explanation:

To solve we must solve like any other linear equation. To do this we must get all variables, in this case the k's, on one side and all the of the constants on the other side.

$\therefore$ $6 k + 5 = 2 k + 1$
$\therefore$ $4 k = - 4$

Now to find $k$ we just divide by the coefficient, in this case $4$

$\therefore k = - 1$