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18 multiple-choice questions and 26 flashcards on Equivalent Linear Expressions, about 12% of the 7th Math: Expressions & Equations bank. Every one carries a written rationale.
Equivalent Linear Expressions is one of 5 chapters in CoStudy's 7th Math: Expressions & Equations bank, and it holds 18 of the bank's 150 multiple-choice questions — roughly 12% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.
Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.
8 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.
Factor: 12x + 18
Answer: D — 6(2x + 3)
D) GCF of 12 and 18 is 6: 6(2x + 3). B) Used 3 instead of full GCF. C) Used 2 instead of full GCF. A) Arithmetic error — 6·6 = 36, not 18.
Distribute: −(x − 5)
Answer: D — −x + 5
D) −1·x = −x; −1·(−5) = +5. B) Sign error on −5. C) Didn't distribute the negative. A) Distributed incorrectly.
Distribute: 0.5(4x − 8)
Answer: A — 2x − 4
A) 0.5·4x = 2x; 0.5·(−8) = −4. B) Forgot to halve the 8. C) Forgot to halve the x. D) Multiplied only the constant.
Factor: 5x + 5y + 10
Answer: C — 5(x + y + 2)
C) GCF of 5, 5, 10 is 5: 5(x + y + 2). B) Forgot to divide 10. A) Didn't factor the 10. D) Wrong GCF.
Simplify: 4x + 7 − 2x + 3
Answer: A — 2x + 10
A) 4x − 2x = 2x; 7 + 3 = 10. B) Summed x terms incorrectly. C) Lost a constant. D) Both errors.
Which is equivalent to 4x + 8?
Answer: D — 4(x + 2)
D) Factor: 4(x + 2) = 4x + 8. B) Yields 4x + 32. C) Yields 8x + 32. A) Different operation.
Distribute: −3(2x − 5)
Answer: D — −6x + 15
D) −3·2x = −6x; −3·(−5) = +15. A) Sign error on constant (forgot negative · negative). C) Sign error on x term. B) Forgot to distribute −3 to the 5.
Are 2(3x + 4) and 6x + 4 equivalent?
Answer: B — No — should be 6x + 8
B) 2(3x + 4) = 6x + 8, not 6x + 4 (forgot to distribute to 4). A/D) Incorrectly assume equivalence. C) Wrong x coefficient.
4 cards from the 26 in this chapter.
Combine: 8y − 3y.
5y.
Factor: 2x + 7. (Hint: GCF?)
Already in simplest form. GCF of 2 and 7 is 1, so no factoring possible beyond the existing form.
Combine: 3x + 5 − 8x − 12.
−5x − 7.
Factor: 8x − 20.
4(2x − 5).
These are a sample. The full Equivalent Linear Expressions chapter runs 44 items with per-chapter progress tracking, on the web and in the iOS app.
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