Class 10 Maths - ICSE
Linear Inequations
The chapter 'Linear Inequations in One Variable' for Class 10 ICSE students builds upon the concept of simple linear equations by introducing inequalities using relation symbols like greater than, less than, or equal to. Students learn to solve inequations algebraically and represent their solution sets using set-builder notation, roster form, and graphically on a real number line. This chapter is fundamental for higher-level algebra and optimization problems. In the ICSE Class 10 Mathematics board examination, it consistently features in Section A as a compulsory, high-scoring question worth 3 to 4 marks, making accuracy in number line representation crucial.
Start Learning FreeKey Concepts
Linear Inequation
An algebraic statement involving a linear expression and an inequality symbol (<, >, ≤, ≥) containing a single variable.
Solution Set
The collection of all values of the variable that satisfy the given inequation, often restricted to a specific replacement set like natural numbers (N), integers (Z), or real numbers (R).
Replacement Set
The universal set from which the values of the variable participating in the inequation are chosen.
Number Line Representation
A graphical method of displaying the solution set on a real number line using thick lines for continuous ranges and solid/hollow dots for discrete values.
Rules of Transposition
Similar to equations, terms can be shifted across the inequality sign, but multiplying or dividing both sides by a negative number reverses the direction of the inequality sign.
Important Formulas
Board Exam Info
In the ICSE Class 10 Mathematics examination, this chapter typically carries about 3 to 4 marks. Questions usually appear as a direct solving problem in Section A. Common question types include solving a single or simultaneous linear inequation for a given replacement set (like integers or real numbers) and representing the final solution on a number line.
Frequently Asked Questions
When do we reverse the inequality sign while solving?
You must reverse the inequality sign (e.g., change < to >) only when you multiply or divide both sides of the inequation by a negative number.
What is the difference between a solid dot and a hollow dot on a number line?
A solid dot is used for 'less than or equal to' (≤) or 'greater than or equal to' (≥) to show that the endpoint is included in the solution. A hollow dot is used for strict inequalities (< or >) to show the endpoint is excluded.
How do I write the answer when the replacement set is Real numbers (R)?
For real numbers, the solution cannot be listed individually, so you must express it in set-builder notation (e.g., {x : x ∈ R, a ≤ x < b}) and show it as a shaded line with appropriate endpoints on the number line.
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