Predict the result
Solve six d plus eight equals five d minus three.

Set up the model
Subtract five d from both sides.
Then subtract eight and check the original sides.

Work the example
After collecting variable terms, d plus eight equals negative three.
The solution is negative eleven; both original sides equal negative fifty eight.

Check the result
Solve three y plus four equals three y.
Take eight seconds to think before the answer appears.
[Eight-second silent pause to work; the answer remains hidden.]
Subtracting three y leaves four equals zero, a contradiction. There is no solution.

Interpret the result
A contradiction means no solution; an identity would require a different conclusion.