91Ó°ÊÓ

The given equation is $18\left(5j−1\right)+29=47$.

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.

$\begin{array}{l}\text{Now,}\\ ⇒18\left(5j−1\right)+29=47\\ ⇒90j−18+29=47\left[\text{UsetheDistributiveProperty}\right]\\ ⇒90j+11=47\left[\text{Combinetheliketerms}\right]\\ ⇒90j+11−11=47−11\left[\text{Subtract}11\text{fromboththesides}\right]\\ ⇒9j=36\\ ⇒\frac{9j}{9}=\frac{36}{9}\left[\text{Divideboththesidesby}9\right]\\ ⇒j=4\end{array}$

The equation is true for$j=4.$

This is a conditional equation.

The solution will be$j=4.$