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23 multiple-choice questions and 11 flashcards on Inequalities and Their Solutions, about 15% of the 6th Math: Expressions & Equations bank. Every one carries a written rationale.
Inequalities and Their Solutions is one of 6 chapters in CoStudy's 6th Math: Expressions & Equations bank, and it holds 23 of the bank's 150 multiple-choice questions — roughly 15% 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.
Solve 2x + 3 = 15.
Answer: A — x = 6
Subtract 3: 2x = 12. Divide by 2: x = 6. (B), (C), (D) miscalculate.
Which value makes 4x = 24 true?
Answer: B — 6
4·6 = 24. (A), (C), (D) don't work.
The inequality x > 5 means x is:
Answer: B — Any value greater than 5
B) Strict inequality — values strictly above 5. A) Equality, not inequality. C) Reversed direction. D) Bounded range, not what x > 5 means.
Word: A roller coaster requires riders to be at least 48 inches tall. Inequality?
Answer: C — h ≥ 48
C) "At least" includes 48: ≥. D) Misses 48 itself. A/B) Wrong direction.
Word: A movie ticket costs at most $12. Which inequality represents the cost c?
Answer: C — c ≤ 12
C) \"At most\" includes the value: c ≤ 12. A) Loses the equality possibility. B/D) Wrong direction.
Solve: x + 6 ≤ 10.
Answer: D — x ≤ 4
D) Subtract 6: x ≤ 4. B) Added instead of subtracted. C) Direction reversal — sign flipped without reason. A) Lost the equality part of ≤.
Which graph represents x ≥ 2 on a number line?
Answer: C — Closed (filled) circle at 2, arrow right
C) ≥ includes 2 (closed circle) and 'greater' goes right. A) Open circle would mean strictly >. B) Wrong direction. D) Wrong direction AND wrong circle.
Which inequality is shown by an open circle at 4 with the arrow shaded to the left?
Answer: D — x < 4
D) Open = strict (not equal); left = less than. A) Wrong direction. C) Closed circle is needed for ≤. B) Wrong direction and circle type.
Solve x/5 = 4.
Answer: C — x = 20
Multiply both sides by 5: x = 20. (A), (B), (D) miscalculate.
Solve: x − 5 > 12.
Answer: C — x > 17
C) Add 5 to both sides: x > 17. A) Subtracted instead of added. B) Half-right — sign flipped erroneously (we only flip when dividing by a negative, not here). D) Multiplied.
4 cards from the 11 in this chapter.
What does '≤' mean?
Less than or equal to.
What does '<' mean?
Less than.
What does '>' mean?
Greater than.
How do you graph x ≤ 5 on a number line?
Closed (filled) circle on 5, arrow extending to the left.
These are a sample. The full Inequalities and Their Solutions chapter runs 34 items with per-chapter progress tracking, on the web and in the iOS app.
Open 6th Math: Expressions & Equations in CoStudy →