Solve 4x + 7 = 23.
Incorrect answer: x = 7.5
Distribute to every term: 3(x + 2) = 3x + 6, not 3x + 2. Never divide by a variable expression without considering whether it could be zero.
Changing only one side of an equation
An equation remains balanced only when equivalent operations are performed on both sides.
The correction
x = 4
Subtract 7 to obtain 4x = 16, then divide by 4.
- Distribute across parentheses and combine like terms on each side.
- Add or subtract the same expression on both sides to gather variable terms.
- Isolate the variable, then check. A false constant statement means no solution; a true identity means every allowed value works.
Try the reasoning in another example
Solve 5x − 4 = 2x + 11.
- Subtract 2x: 3x − 4 = 11.
- Add 4 and divide by 3: 3x = 15, so x = 5.
- Both original sides equal 21 at x = 5.
Answer: x = 5
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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