91Ó°ÊÓ

The given equation is $12\left(6h − 1\right) = 8\left(8h + 5\right) − 4$.

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.

We have,

$12(6h−1)=8(8h+5)−4$

Expand $12(6h−1):72h−12$

Expand $8(8h+5)−4:64h+36$

$72h−12=64h+36$

Add 12 to both sides

$72h−12+12=64h+36+12$

Simplify

$72h=64h+48$

Subtract $64h$from both sides

$72h−64h=64h+48−64h$

Simplify

$8h=48$

Divide both sides by 8

$\frac{8h}{8}=\frac{48}{8}$

Simplify

$h=6$

The equation is true for $h=6$.

The equation is a conditional equation.

The solution of the equation will be $h=6$.