91Ó°ÊÓ

The given equation is $30\left(2n−1\right)=5\left(10n+8\right)$.

We have to classify the equation as a conditional equation, an identity, or a contradiction.

Also, we have to state the solution of the equation.

We know,

• An equation that is true for one or more values of the variable and false for all other values of the variable is a conditional equation.
• An equation that is true for any value of the variable is called an identity. The solution of identity is all real numbers
• An equation that is false for all values of the variable is called a contradiction. A contradiction has no solution.

$\begin{array}{l}\text{Now,}\\ ⇒30\left(2n−1\right)=5\left(10n+8\right)\\ ⇒60n−30=5n+40\left[\text{UsetheDistributiveProperty}\right]\\ ⇒60n−30+30=50n+40+30\left[\text{Add}30\text{fromboththesides}\right]\\ ⇒60n=50n+70\\ ⇒50m−88+88=72+88\left[\text{Subtract}50n\text{fromboththesides}\right]\\ ⇒60n−50n=50n+70−50n\\ ⇒10n=70\\ ⇒\frac{10n}{10}=\frac{70}{10}\left[\text{Divideboththesidesby10}\right]\\ ⇒n=7\end{array}$

The equation is true for n =7.

This is a conditional equation.

The solution will be$n=7$