Linear Inequalities

 Linear Inequalities        practice these sums👈

✅ 1. Definition:

A linear inequation is an algebraic statement showing inequality between two expressions, involving a variable raised to the power of 1.

Examples:

• $x + 3 < 7$

• $2x - 5 \geq 3$

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✅ 2. Symbols of Inequality:

Symbol	Meaning
$<$	Less than
$\le$	Less than or equal to
$>$	Greater than
$\geq$	Greater than or equal to

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✅ 3. Solution of a Linear Inequation:

Solving means finding all values of the variable that make the inequality true.

Example:
Solve: $x + 4 < 9$

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✅ 4. Rules for Solving Inequations:

Rule	Description
Add/Subtract same number	Inequality sign remains same
Multiply/Divide by a positive number	Sign remains same
Multiply/Divide by a negative number	Reverse the inequality sign

Example:
Solve: $-2x > 6$
👉 Divide by -2 → $x < -3$        (sign reversed)

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✅ 5. Representation on Number Line:

• Open circle (○) for < or >

• Filled circle (●) for ≤ or ≥

• Arrow shows the direction of values.