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27 multiple-choice questions and 17 flashcards on Solving One-Variable Equations, about 18% of the 6th Math: Expressions & Equations bank. Every one carries a written rationale.
Solving One-Variable Equations is one of 6 chapters in CoStudy's 6th Math: Expressions & Equations bank, and it holds 27 of the bank's 150 multiple-choice questions — roughly 18% 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.
10 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.
Write 'the quotient of a number n and 5' as an expression.
Answer: C — n / 5
Quotient = division. (A) multiplies; (B) subtracts; (D) adds.
Solve: 2x + 5 = 17.
Answer: A — x = 6
A) Subtract 5: 2x = 12. Divide by 2: x = 6. B) Subtracted only. C) Added instead of subtracted. D) Forgot to divide by 2.
Word: Maria has $50. She buys n notebooks at $4 each and now has $26. Equation?
Answer: D — Both B and C
D) Both B and C are equivalent setups: 50 − 4n = 26 is the spending model; 26 + 4n = 50 is the inverse. A) Adds 4n instead of subtracting.
Simplify 5x − 3x + 2.
Answer: D — 2x + 2
5x − 3x = 2x, +2 → 2x + 2. (B), (C), (A) misapply.
Solve: x − 8 = 15.
Answer: D — x = 23
D) Add 8 to both sides: x = 23. A) Subtracted instead of added. C) Off-by-one error. B) Sign error — direction reversed.
Solve: x + 9 = 14.
Answer: C — x = 5
C) Subtract 9 from both sides: x = 5. A) Added instead of subtracted. B) Just took the right side. D) Off-by-one error.
Word: 6 friends share x marbles equally; each gets 9. How many marbles total?
Answer: C — 54
C) x/6 = 9, so x = 54. A) Added: 6 + 9. B) Subtracted. D) Inverted division.
Which is equivalent to 6x + 12?
Answer: D — All of the above
6(x+2) = 6x + 12 = 6(x) + 12 = 6x + 6·2. All are equivalent forms.
Solve x / 4 = 5.
Answer: D — 20
D) Multiply both sides by 4: x = 20. B) Skipped the multiplication. C) Confused with x = 5/4. A) Added 4 + 5.
Which is equivalent to 3(x + 4)?
Answer: B — 3x + 12
Distribute 3 over both terms: 3·x + 3·4. (A), (C), (D) misapply.
4 cards from the 17 in this chapter.
Worked example: Solve 4x = 28.
Step 1 — x is multiplied by 4. Step 2 — Inverse: divide BOTH sides by 4. Step 3 — 4x ÷ 4 = 28 ÷ 4 → x = 7. Check: 4 · 7 = 28 ✓. Answer: x = 7.
What is an 'equation'?
A math statement saying two expressions are EQUAL. Has an equals sign. Like x + 5 = 12.
What does 'solve an equation' mean?
Find the value of the variable that makes the equation true.
What's the inverse operation to multiplication?
Division.
These are a sample. The full Solving One-Variable Equations chapter runs 44 items with per-chapter progress tracking, on the web and in the iOS app.
Open 6th Math: Expressions & Equations in CoStudy →