Solving and Graphing Inequalities
Key rules, graphing conventions, and word-problem translations for solving linear inequalities on the PSAT.
Keyboard Shortcuts
💡 Pro tip: Use keyboard shortcuts for faster studying!
Study Smart Tips for Solving and Graphing Inequalities
Master these concepts using proven study techniques that actually work:
Active Recall
Test yourself before flipping each card to strengthen memory retention
Spaced Repetition
Review difficult cards more frequently than easy ones
Multiple Sessions
Break study time into shorter, focused sessions
Explain Aloud
Verbalize answers to reinforce understanding
Questions Covered in This Set
10 cards to master
When do you flip the inequality symbol?
Only when you multiply or divide BOTH sides by a negative number. Adding or subtracting a negative never flips it.
Solve: -2x > 10
x < -5 (divide by -2 and flip the symbol)
Solve: 5 - 3x ≥ 17
Subtract 5: -3x ≥ 12; divide by -3 and flip: x ≤ -4
Open circle vs. closed circle on a number line
Strict symbols (< , >) get an open ○ circle; ≤ and ≥ get a closed ● dot because the line underneath means 'filled in'.
How do you graph x ≥ 3?
Closed dot at 3 with an arrow shading to the right.
How do you solve a compound inequality like -7 ≤ 2x - 1 < 5?
Do the same operation to all three parts: add 1 → -6 ≤ 2x < 6; divide by 2 → -3 ≤ x < 3.
What happens if you divide all three parts of a compound inequality by a negative?
Flip BOTH symbols; the statement reads backwards (e.g., 4 > x > -1 is the same as -1 < x < 4).
Translate: 'at least', 'at most', 'more than', 'fewer than'
at least → ≥; at most / no more than → ≤; more than → >; fewer than → <
Rideshare: $3.50 base + $1.25/mile, at most $20. Greatest whole miles?
3.50 + 1.25m ≤ 20 → m ≤ 13.2 → answer 13 (round DOWN in context).
Pro tip to avoid flipping altogether
Move the variable to the side that keeps its coefficient positive, then solve normally.
