Class 11: Linear Inequalities

Algebraic Solutions & Graphical Representation

Definition	Two real numbers or algebraic expressions related by symbol $$<, >, \le$$or$$\ge$$ form an inequality.
Types	Strict Inequality: Uses $$<$$or$$>$$(e.g.,$$ax + b < 0$$) Slack Inequality: Uses $$\le$$or$$\ge$$(e.g.,$$ax + b \ge 0$$)
Solution	Values of the variable ($$x$$) which make the inequality a true statement.

Rule 1 (Addition/Subtraction)	Equal numbers may be added to (or subtracted from) both sides without affecting the sign of inequality.
Rule 2 (Multiplication/Division)	1. Both sides can be multiplied/divided by same positive number (Sign remains same). 2. If multiplied/divided by a negative number, the inequality sign is reversed (e.g., $$3 > 2$$but$$-3 < -2$$).

Strict Inequality ($$x < a$$or$$x > a$$)	Put an open circle ($$\circ$$) on number $$a$$and darken line to the left (for$$<$$) or right (for $$>$$).
Slack Inequality ($$x \le a$$or$$x \ge a$$)	Put a dark/filled circle ($$\bullet$$) on number $$a$$and darken line to the left (for$$\le$$) or right (for $$\ge$$).