Chapter 4.3, Problem 9MRE

To determine

To simplify the equation

  $7n-5=2n$

Answer to Problem 9MRE

  $n=1$

Explanation of Solution

Given:

  $7n-5=2n$

Concept Used:

• In an equation, like terms are added or subtracted with each other.
• Any value if added, subtracted, multiplied or divided on the left hand side of the equation, then it should also be added or subtracted on right hand side so that the equation is balanced.

Calculation:

To simplify the equation

  $7n-5=2n$

First subtract each side of the equation by $2n$ as,

  $\begin{array}{l}7n-5-2n=2n-2n\\ \Rightarrow 5n-5=0\end{array}$

Now, adding $5$ on both sides as,

  $\begin{array}{l}5n-5+5=0+5\\ \Rightarrow 5n=5\end{array}$

Now divide the remaining equation by $5$ on both sides as,

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

Thus, the simplified equation becomes

  $n=1$