91Ó°ÊÓ

The given equation is $9\left(4k − 7\right) = 11\left(3k + 1\right) + 4$.

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.

$9(4k−7)=11(3k+1)+4$

Expand $9(4k−7):36k−63$

Expand $11(3k+1)+4:33k+15$

$36k−63=33k+15$

Add 63 to both sides

$36k−63+63=33k+15+63$

Simplify

$36k=33k+78$

Subtract $33k$from both sides

$36k−33k=33k+78−33k$

Simplify

Divide both sides by 3

Simplify

The equation is true for $k=26.$

The equation is a conditional equation.

The solution to the equation will be$k=26.$