Start with this short video, then scroll down for the full guide.
Why This Matters for Nursing: "Give no more than 400 mg daily." "Patient must weigh at least 50 kg for this dose." Healthcare is full of ranges and limits. Understanding inequalities helps you interpret orders and stay within safe parameters.
An inequality compares values that are NOT necessarily equal:
| Symbol | Meaning | Example | In Words |
|---|---|---|---|
| < | Less than | x < 5 | x is less than 5 |
| > | Greater than | x > 3 | x is greater than 3 |
| ≤ | Less than or equal to | x ≤ 10 | x is at most 10 |
| ≥ | Greater than or equal to | x ≥ 7 | x is at least 7 |
The alligator eats the bigger number! 🐊
5 > 3 → The open mouth faces 5 (the bigger one)
"Less than = Littler on Left" x < 5 means x is the SMALLER value (on the left of the number line)
AT LEAST / AT MOST: - "At LEAST" means you need that much OR MORE → ≥ - "At MOST" means that's the MAX allowed → ≤
Solve inequalities just like equations with ONE important exception:
⚠️ When you multiply or divide by a NEGATIVE number, FLIP the inequality sign!
Problem: x + 4 > 9
Step 1 — Solve just like an equation. The goal is the same: isolate x. Subtract 4 from both sides. - Left: x + 4 - 4 = x - Right: 9 - 4 = 5
Step 2 — Write the inequality. x > 5.
Step 3 — Interpret. x > 5 means x can be ANY number greater than 5 (like 5.001, 6, 100, etc.) — but NOT 5 itself.
Answer: x > 5
The worked examples and practice problems are the part that actually prepares you for the TEAS.
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