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9 multiple-choice questions and 20 flashcards on Solving Linear Equations and Inequalities, about 6% of the High School Algebra 1 bank. Every one carries a written rationale.
Solving Linear Equations and Inequalities is one of 8 chapters in CoStudy's High School Algebra 1 bank, and it holds 9 of the bank's 150 multiple-choice questions — roughly 6% 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.
6 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 for x: 3x + 7 = 22.
Answer: B — 5 (subtract 7: 3x = 15; divide by 3: x = 5)
Two-step linear equation. Subtract 7 from both sides: 3x = 15. Divide both sides by 3: x = 5. Foundation of solving equations: isolate variable using inverse operations.
If x² + 3x = 0, what are the solutions?
Answer: C — x = 0 or x = -3 (factor: x(x+3) = 0; zero product property)
Factor out common x: x(x+3) = 0. Zero product property: if AB=0, then A=0 or B=0. So x=0 or x+3=0 → x=-3. Always factor before using quadratic formula when possible.
Solve for x: -6x + 2 = -16.
Answer: D — x = 3
A) Sign error: divided -18 by 6 instead of -6. B) Forgot to subtract 2 first; divided 2 by -6. C) Sign error after dividing by -6. D) Subtract 2: -6x = -18; divide by -6: x = 3. Always reverse the constant first, then the coefficient.
What is the vertex of the parabola y = (x-2)² + 3?
Answer: B — (2, 3) — vertex form y = a(x-h)² + k has vertex at (h, k)
Vertex form: y = a(x-h)² + k. Vertex at (h, k). Here h=2, k=3 → vertex (2, 3). Note sign: (x-2) means h=+2. If a>0, parabola opens up (minimum). If a<0, opens down (maximum).
Which equation represents a line parallel to y = 3x + 2?
Answer: E — y = 3x - 7 (same slope, different y-intercept)
Parallel lines have the SAME slope. Slope of y = 3x + 2 is 3. y = 3x - 7 also has slope 3 → parallel. Perpendicular lines have NEGATIVE RECIPROCAL slopes (e.g., -1/3 for slope 3).
What is the slope of a horizontal line?
Answer: B — 0 (no rise; the y-values don't change)
Horizontal line: y = constant. Slope = rise/run = 0/run = 0. No vertical change. Compare vertical line (x = constant): slope is UNDEFINED (run = 0, division by zero).
4 cards from the 20 in this chapter.
When does a linear equation have no solution?
When variables cancel and a false statement remains (e.g., 2x + 3 = 2x + 5 → 3 = 5).
Solve: |x − 3| = 7.
x − 3 = 7 or x − 3 = −7 → x = 10 or x = −4.
Solve: 4(x + 2) = 20.
4x + 8 = 20 → 4x = 12 → x = 3.
Solve: 3x + 2 > 11.
3x > 9 → x > 3.
These are a sample. The full Solving Linear Equations and Inequalities chapter runs 29 items with per-chapter progress tracking, on the web and in the iOS app.
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