Chapter 5.3, Problem 38E

To determine

To calculate:

The solution of the following equation and categorize it to one solution, no solution or infinitely many solutions:

  $3n+2=2\left(n-3\right)$

Answer to Problem 38E

The solution of $3n+2=2\left(n-3\right)$ is $n=-8$

Explanation of Solution

Given information:

  $3n+2=2\left(n-3\right)$

Calculation:

The given equation is as:

  $3n+2=2\left(n-3\right)$

Simplify the bracket first:

  $\begin{array}{l}3n+2=2\left(n-3\right)\\ 3n+2=2n-6\end{array}$

Subtract $2n$ from both sides of equations:

  $\begin{array}{l}3n-2n+2=2n-2n-6\\ n+2=-6\end{array}$

Subtract $2$ from both sides of equations:

  $\begin{array}{l}n+2-2=-6-2\\ n=-8\end{array}$