Linear Inequalities:Class 11 Maths NCERT Chapter 6

Key Features of NCERT Material for Class 11 Maths Chapter 6 – Linear Inequalities

In the previous Chapter 5:Complex Numbers and Quadratic Equations we have learned about complex numbers and its properties.In this Chapter 6:Linear Inequalities we will study about inequalities between two quantities and solution of an inequality.

Quick revision notes

Inequation 

An announcement including factors and the indication of disparity viz. >, <, ≥ or ≤ is called an inequation or a disparity. 

Mathematical Inequalities 

Inequalities which don’t contain any factor is called mathematical inequalities, for example 3 < 7, 2 ≥ – 1, and so forth. Exacting Inequalities which contains factors are called strict inequalities for example x – y > 0, x > 5, and so forth.

Linear Inequation of One Variable 

Take a non-zero real number ‘a’ and a variable ‘x’. At that point, inequalities of the structure ax + b > 0, ax + b < 0, ax + b ≥ 0 and ax + b ≤ 0 are known as linear inequalities in a single variable. 

Linear Inequation of Two Variables

Let a, b be non-zero genuine numbers and x, y be variables. At that point, inequation of the structure hatchet + by < c, hatchet + by > c, hatchet + by ≤ c and hatchet + by ≥ c are known as linear imbalances in two variables x and y. 

Solution of an Inequality 

The value(s) of the variable(s) which makes the disparity a genuine explanation is called its solutions. The arrangement of all solutions of an imbalance is known as the solution set of the disparity. 

Comprehending Linear Inequations in One Variable 

Same number might be included (or deducted) to the two sides of an inequation without changing the indication of disparity. 

The two sides of an inequation can be multiplied (or isolated) by a similar positive genuine number without changing the indication of imbalance. Be that as it may, the indication of disparity is switched when the two sides of an inequation are multiplied or isolated by a negative number. 

Portrayal of Solution of Linear Inequality in One Variable on a Number Line 

To speak to the solution of a linear disparity in one variable on a number line. We utilize the accompanying calculation. 

On the off chance that the imbalance includes ‘>’ or ‘<‘ we draw an open circle (O) on the number line, which demonstrates that the number comparing to the open circle is excluded from the solution set.

If the inequality involves ‘≥’ or ‘≤’ we draw a dark circle (•) on the number line, which indicates the number corresponding to the dark circle is included in the solution set.

Representation of the Solution of Linear Inequality in One or Two Variables Graphically

To speak to the solution of linear imbalance in a couple of variables graphically in a plane, we utilize the accompanying calculation. 

In the event that the disparity includes ‘<‘ or ‘>’, we draw the chart of the line as dotted line to show that the focuses on the line are excluded from the solution sets. 

In the event that the disparity includes ‘≥’ or ‘≤’, we draw the chart of the line as a dim line to demonstrate the focuses on the line is incorporated from the solution sets. 

Solution of a linear disparity in one variable can be spoken to on number line just as in the plane yet the solution of a linear imbalance in two variables of the sort hatchet + by > c, hatchet + by ≥ c,ax + by < c or hatchet + by ≤ c (a ≠ 0, b ≠ 0) can be spoken to in the plane as it were. 

At least two inequalities taken together include an arrangement of inequalities and the solution of the arrangement of inequalities are the solution regular to all the inequalities involving the framework.