Solve x − 8 = 6.
Incorrect answer: x = −2
Changing only one side breaks the equality. The goal is to undo the operation, not repeat it: x + 7 = 19 needs subtraction, not another addition of 7.
Using the same operation to undo an equation
Undo addition with subtraction and multiplication with division. Check by substituting into the original equation.
The correction
x = 14
Add 8 to both sides.
- Identify the operation performed on the variable.
- Apply the inverse operation equally to both sides.
- Substitute the answer into the original equation to verify it.
Try the reasoning in another example
Solve 4x = 28.
- Divide both sides by 4.
- Check 4 × 7 = 28.
Answer: x = 7
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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2 questions · No time limitCheck this step for yourself
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