Undo a Fractional Coefficient

Supplied materials

• Paper or a browser scratch area; a calculator is optional unless rounding is requested.
• Supplied teaching case: Solve x/2+3=5. Candidate answers: (A) 3 (B) 4 (C) 5 (D) 8.
• Independent check inputs: Solve x/2+4=7. Candidate answers: (A) 12 (B) 5 (C) 6 (D) 7.

Learn the idea

Solving means finding inputs that make a relationship true. Balanced operations preserve equality, whereas inequality direction must reverse when multiplication or division by a negative number reverses number-line order. A coefficient can be a fraction, such as one half. Remove an added constant first, then undo the fractional multiplication using its reciprocal on both sides.

Here is the method on the supplied teaching case. Subtract 3 from both sides to get x/2=2. Multiply both sides by 2: x=4. Check: 4/2+3=5.0.

Perform the same operation on both sides, including the constant. Verify the result in the original equation; an apparently simplified line may hide a missed term or an arithmetic sign mistake.

1. Write or sketch the supplied teaching case, labeling its quantities and restrictions.
2. Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
3. Solve the independent check with its changed inputs before revealing feedback.
4. Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.

Check your reasoning

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Take it further

Changed-input task: Solve x/2+10=19. Candidate answers: (A) 17 (B) 18 (C) 19 (D) 36. Show the mathematical reason, not only the selected answer. Expected result: 18. Subtract 10 from both sides to get x/2=9. Multiply both sides by 2: x=18. Check: 18/2+10=19.0.

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