## 6. Linear Inequalities # LINEAR INEQUALITIES CLASS 11 MATHS

## Summary

Two real numbers or two algebraic expressions related by the symbols <, >, ≤ or ≥ form an inequality.

Equal numbers may be added to (or subtracted from ) both sides of an inequality.

Both sides of an inequality can be multiplied (or divided ) by the same positive number. But when both sides are multiplied (or divided) by a negative number, then the inequality is reversed.

The values of x, which make an inequality a true statement, are called solutions of the inequality.

To represent x < a (or x > a) on a number line, put a circle on the number a and dark line to the left (or right) of the number a.

To represent x ≤ a (or x ≥ a) on a number line, put a dark circle on the number a and dark the line to the left (or right) of the number x.

If an inequality is having ≤ or ≥ symbol, then the points on the line are also included in the solutions of the inequality and the graph of the inequality lies left (below) or right (above) of the graph of the equality represented by dark line that satisfies an arbitrary point in that part.

If an inequality is having < or > symbol, then the points on the line are not included in the solutions of the inequality and the graph of the inequality lies to the left (below) or right (above) of the graph of the corresponding equality represented by dotted line that satisfies an arbitrary point in that part.

The solution region of a system of inequalities is the region which satisfies all the given inequalities in the system simultaneously.

## Lecture - 1

• Basics of Inequalities, Strict and Slack inequalities
• Working with inequalities: Adding positive or negative numbers, Subtracting positive or negative numbers, Multiplying by positive or negative numbers and Dividing by positive or negative numbers
• Representing Real numbers in form of open intervals and closed intervals
• NCERT Exercise 6.1 (Q1 to Q20)

## Lecture - 2

• NCERT Exercise 6.1 (Q21 to Q26)
• Graphical Representation of Inequalities
• NCERT Exercise 6.2 (Q1 to Q7)
• NCERT Exercise 6.2 (Q9 & Q10)

## Lecture - 3

• Working with system of inequalities
• NCERT Exercise 6.3 (Q10 to Q15)

## Lecture - 4

• Working with double inequalities
• NCERT Miscellaneous Exercise (Q1 to Q14)