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Class 11 Math Linear Inequalities Notes PDF
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Key Points
• Inequality – A statement involving variables and the sign of inequality like >, <, ≥ or ≤ is called an inequality.
• Numerical inequalities – Inequalities which do not contain any variable.
Ex – 3 < 7, 2 ≥ −1 etc.
• Literal inequalities – Inequalities which contain variables.
Ex – x − y > 0, x ≥ 5 etc.
Linear inequality of one variable
Let a be non-zero real number and x be a variable. Then, inequalities of the form
ax + b > 0,
ax + b < 0,
ax + b ≥ 0 and
ax + b ≤ 0
are known as linear inequalities in one variable.
Linear inequality of two variables
Let a, b be non-zero real numbers and x, y be variables. Then inequality of the form
ax + by < c,
ax + by > c,
ax + by ≤ c and
ax + by ≥ c
are known as linear inequalities in two variables x and y.
Solution of an inequality
The values of the variables which make the inequality a true statement is called its solutions.
Solving linear inequalities in one variable
• Same number may be added (or subtracted) to both sides of an inequality without changing the sign of inequality.
• Both sides of an inequality can be multiplied (or divided) by the same positive real number without changing the sign of inequality.
• Sign of inequality is reversed when both sides of an inequality are multiplied or divided by a negative number.
Representation of solution of linear inequality in one variable on a Number Line
For this we use following algorithm:
• If the inequality involves > or < we draw an open circle (○) on the number line, which indicates that the number corresponding to the open circle is not included in 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.
Graphical representation of the solution of linear inequality in one or two variables
For this we use following algorithm:
• If the inequality involves < or > we draw the graph of the line as dotted line to indicate that the points on the line are not included from the solution sets.
• If the inequality involves ≥ or ≤ we draw the graph of the line as a dark line to indicate the points on the line is included from the solution sets.