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중단원 평가 · Unit Assessment

Master Inequalities

From basics to tricky word problems — understand every type, build your intuition.

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Core Concepts

Key Rules to Know

① Inequality Basics

An inequality compares two expressions using <, ≤, >, ≥. The solution is a range of values, not a single answer.

🔑 Memory Hook RANGE not POINT — inequalities give a set of answers.

② Adding / Subtracting

You can add or subtract the same number from both sides — the inequality sign does NOT flip.

🔑 Memory Hook ADD/SUB = SAFE. Sign stays the same.

③ Multiply / Divide by POSITIVE

Multiplying or dividing both sides by a positive number → sign stays the same.

🔑 Memory Hook POSITIVE × ÷ = SAFE. No flip.

④ ⚠️ Multiply / Divide by NEGATIVE

Multiplying or dividing both sides by a negative number → FLIP the sign! This is the #1 mistake.

🔑 Memory Hook NEGATIVE × ÷ = DANGER → FLIP the sign!

⑤ Compound Inequalities

Like \(a < x < b\): do the same operation to all three parts simultaneously.

🔑 Memory Hook THREE-PART: do it to ALL three at once.

⑥ Word Problem Strategy

Let x = the unknown. Set up the inequality from the condition. Solve, then check if the answer makes real-world sense.

🔑 Memory Hook LET → SET UP → SOLVE → CHECK sense.