Solving & Interpreting Inequalities

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.

What You Need to Know

An inequality compares values that are NOT necessarily equal:

Key Language

• "At least" → ≥ (greater than or equal to)
• "At most" → ≤ (less than or equal to)
• "No more than" → ≤
• "No less than" / "Minimum" → ≥
• "Maximum" → ≤

🧠 Memory Trick

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 → ≤

Solving Inequalities

Same as Equations, BUT...

Solve inequalities just like equations with ONE important exception:

⚠️ When you multiply or divide by a NEGATIVE number, FLIP the inequality sign!

Example: -2x > 6

• Divide by -2: x < -3 (sign flipped!)
• Answer: x < -3

✏️ Worked Examples

Example 1: Basic Inequality

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

Example 2: With Multiplication

Problem: 3x ≤ 18