Solve 5x + 1 = 2x + 10.
Incorrect answer: x = 9/7
If the variable cancels, do not automatically report x = 0. A true constant statement means all real values work; a false one means none work.
Dropping variable terms or forcing a solution
Collect variable terms with balanced operations. If variables cancel, decide whether the remaining statement is true.
The correction
x = 3
Subtract 2x and 1 to get 3x = 9.
- Expand parentheses and combine like terms within each side.
- Subtract a variable term from both sides, then isolate the remaining variable.
- Check in the original equation; if the variable disappears, decide whether the remaining statement is true or false.
Try the reasoning in another example
Solve 2(x + 4) = 2x + 8.
- Expand to 2x + 8 = 2x + 8.
- Subtracting both matching expressions gives 0 = 0.
Answer: All real numbers
Explain why each step preserves the quantity or relationship. If you can compute the answer but cannot explain the step, revisit the model before adding more questions.
The short check below reuses the first example as a retrieval question and adds a second question. It checks this method; it does not establish a grade level.
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