In the following exercise, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution.

$18u-51=9(4u+5)-6(3u-10)$

The given equation is $18u-51=9(4u+5)-6(3u-10)$.

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,

$18u-51=9(4u+5)-6(3u-10)$

Expand $9(4u+5)-6(3u-10):18u+105$

$18u-51=18u+105$

Add 51 to both sides

$18u-51+51=18u+105+51$

Simplify

$18u=18u+156$

Subtract $18u$from both sides

$18u-18u=18u+156-18u$

Simplify

$0\ne 156$

The sides are not equal.

Therefore, the equation is a contradiction.

Hence, No Solution