A reliable method
Substitute numerical values with parentheses, distribute multiplication over an entire sum, and combine only terms with the same variable part.
The common trap
The expression 4(x + 2) includes four copies of both x and 2. Changing it to 4x + 2 loses three copies of the constant.
Check and transfer
Evaluate an original expression and its simplified form at the same convenient input. Agreement is a useful check, although one example does not prove an identity.
Worked comparison: why the alternative fails
Expand 4(x + 2) to 4x + 8. The alternative 4x + 2 matches only one copy of the constant. At x = 1 the original is 12 but the incorrect form gives 6; a single counterexample disproves that proposed identity.
Transfer and explain
Simplify 5x + 3 − (2x − 4): 3x + 7. Contrast the sign change on the constant with the subtraction of the x coefficients.
A workshop estimates supply cost with C = 4n + 3m. If n = 3 and m = 3, what is C?
- Replace n and m with their stated values.
- Calculate each product before combining the costs.
- The requested value is 21. Check its units and meaning against the original question.
Compare the other answer choices
Omit the coefficient four on n.
Omit the coefficient three on m.
Multiply the two terms instead of adding them.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
GED Mathematical Reasoning overviewSiyavula Grade 10 mathematics foundation reference