Common Mistakes
Algebra I · Honors Math · Linear inequalities and systems
Real mistakes students make on systems of linear inequalities—and how to catch and fix them.
Focus for this topic: Find and interpret regions that satisfy systems of inequalities.
Frequent mistakes
### 1. Not flipping when multiplying/dividing by a negative
What it looks/sounds like: Inequality stays facing the same way after multiplying or dividing by a negative.
Why it happens: Students apply equation habits to inequalities.
How to fix: Circle the negative multiplier, flip the inequality on purpose, and restate the new inequality.
### 2. Open vs closed boundary mistakes
What it looks/sounds like: Solid/dashed line or open/closed circle does not match < vs ≤ (or > vs ≥).
Why it happens: Graphing habits focus on slope/intercept and ignore inclusion.
How to fix: Say “included or not?” before drawing the boundary, then shade.
### 3. Shading the wrong side
What it looks/sounds like: Correct boundary but the wrong half-plane or number-line ray.
Why it happens: Students guess from a picture instead of testing a point.
How to fix: Test (0,0) or another easy point in the original inequality and shade accordingly.
### 4. Compound inequality treated as two unrelated statements
What it looks/sounds like: Solving only one part of a compound inequality, or joining parts with the wrong connector.
Why it happens: AND/OR language is ignored while algebra runs.
How to fix: Rewrite the compound in words (“both true” vs “either true”), then solve each part.
### 5. Story language reversed
What it looks/sounds like: “At least / at most / no more than” mapped to the wrong symbol.
Why it happens: Everyday English is translated by feel instead of a fixed dictionary.
How to fix: Keep a mini chart: at least → ≥, at most → ≤, fewer than → <, more than → >.
How to avoid them
1. Restate what 2.5 asks in one sentence before computing. 2. Name the method or representation you will use. 3. Define variables with units before writing symbols. 4. Check one easy special case, diagram estimate, or unit/domain check after a long solution. 5. Ask: does this answer match the required form and the prompt?
Quick self-check
- [ ] I can name two mistakes for 2.5
- [ ] I can explain why one of those mistakes happens
- [ ] I can fix one wrong solution by naming the broken step
- [ ] I can check that my final form matches what the prompt asked
Related materials
- Parent Guide, Exam Strategy, and Study Guide for 2.5 (same folder)
- Review and practice-test tiers under this topic when present