Which operation should you apply to both sides of 4x = 28 to solve for x?
ASubtract 4
BAdd 4
CMultiply by 4
DDivide by 4
4x means 4 times x, so the operation attached to x is multiplication by 4. The inverse of multiplication is division, so you divide both sides by 4: 4x ÷ 4 = 28 ÷ 4, giving x = 7. Subtracting 4 would not undo multiplication.
Question 2 True / False
To solve x - 9 = 3, you should subtract 9 from both sides.
TTrue
FFalse
Answer: False
To undo subtraction of 9, you add 9 to both sides: x - 9 + 9 = 3 + 9, giving x = 12. Subtracting 9 again would apply the same operation rather than the inverse, producing x - 18 = -6 and moving further from isolating x.
Question 3 Short Answer
A student solves 5x = 30 by subtracting 5 from both sides, arriving at 5x - 5 = 25 and concluding x = 5. Is this correct? Explain why or why not.
Think about your answer, then reveal below.
Model answer: No. 5x = 30 means 5 times x equals 30. To isolate x, divide both sides by 5: x = 30 ÷ 5 = 6. Subtracting 5 does not undo multiplication — it just shifts the equation without isolating x.
The student applied the wrong inverse operation. Multiplication is undone by division, not subtraction. Substituting the student's answer back in confirms the error: 5 × 5 = 25, not 30. Checking by substitution is the reliable way to catch this kind of mistake.