Introduction to Inequalities

 What are Inequalities?


In algebra, not all expressions are equal — some are greater or less than others. Inequalities help us compare values that are not exactly equal.


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🔸 What is an Inequality?


An inequality is a mathematical sentence that shows the relationship between two expressions using comparison symbols.


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🔸 Common Inequality Symbols


Symbol Meaning Example


> Greater than x > 4

< Less than x < 7

≥ Greater than or equal to x ≥ 2

≤ Less than or equal to x ≤ 5


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🔸 Difference Between Equations and Inequalities


An equation gives one exact answer:

  ✅ x = 3


An inequality gives many possible answers:

  ✅ x > 3 (x could be 4, 5, 100…)


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🔸 Solving Inequalities


Solving inequalities is almost the same as solving equations:


You can add, subtract, multiply, or divide both sides.


BUT, if you multiply or divide by a negative number, flip the sign.


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✅ Examples


Example 1:

Solve x + 4 < 9

Step: Subtract 4 from both sides

Answer: x < 5


Example 2:

Solve –2x > 6

Step: Divide both sides by –2 (and flip the sign!)

Answer: x < –3


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📝 Practice Questions


Try solving these on your own:


1. x – 3 ≤ 7

2. 2x + 1 > 9

3. –3x ≤ 12


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📘 Want more lessons and practice?:

Visit: https://easymathsteps.blogspot.com

Or use: www.easymathsguid.com.ng


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