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Solve the Following Inequalities and Represent the Solution Graphically on Number Line: 3x – 7 > 2(X – 6), 6 – X > 11 – 2x - CBSE (Arts) Class 11 - Mathematics

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Question

Solve the following inequalities and represent the solution graphically on number line:

3x – 7 > 2(x – 6), 6 – x > 11 – 2x

Solution

3x – 7 > 2(x – 6)

⇒ 3x – 7 > 2x – 12

⇒ 3x – 2> – 12 + 7

⇒ x > –5 … (1)

6 – x > 11 – 2x

⇒ –x + 2x > 11 – 6

⇒ x > 5 … (2)

From (1) and (2), it can be concluded that the solution set for the given system of inequalities is `(5, oo)`. The solution of the given system of inequalities can be represented on number line as

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Solution Solve the Following Inequalities and Represent the Solution Graphically on Number Line: 3x – 7 > 2(X – 6), 6 – X > 11 – 2x Concept: Graphical Solution of Linear Inequalities in Two Variables.
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