Chapter 2.3, Problem 42E

To determine

To calculate:

The value of $n$ and check the solution:

  $-3n+2=2n-3$

Answer to Problem 42E

The value of $n$ is $1$

Explanation of Solution

Given information:

  $-3n+2=2n-3$

Calculation:

The given equation is:

  $-3n+2=2n-3$

Take all terms of $n$ on one side:

  $\begin{array}{l}-3n+2=2n-3\\ -3n-2n+2=-3\\ -5n+2=-3\end{array}$

Subtract $2$ from both sides of equations:

  $\begin{array}{l}-5n+2-2=-3-2\\ -5n=-5\end{array}$

Divide by $-5$ :

  $\begin{array}{l}-5n=-5\\ \frac{-5}{-5}n=\frac{-5}{-5}\\ n=1\end{array}$

Check the solution as: put $n=1$ in $-3n+2=2n-3$ :

  $\begin{array}{l}-3n+2=2n-3\\ -3\left(1\right)+2=2\left(1\right)-3\\ -3+2=2-3\\ -1=-1\end{array}$

It’s verified.