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Solve Each of the Following System of Equations in R. 2x − 7 > 5 − X, 11 − 5x ≤ 1 - Mathematics

Solve each of the following system of equations in R. 

2x − 7 > 5 − x, 11 − 5x ≤ 1

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Solution

\[x + 3 > 0\]
\[ \Rightarrow x > - 3\]
\[ \Rightarrow x \in \left( - 3, \infty \right) . . . \left( i \right)\]
\[\text{ Also }, 2x < 14\]
\[ \Rightarrow x < 7 \left[ \text{ Dividing both the sides by } 2 \right]\]
\[ \Rightarrow x \in \left( - \infty , 7 \right) . . . \left( ii \right)\]
\[\text{ Thus, the solution of the given set of inequalities is the intersection of } \left( i \right) \text{ and } \left( ii \right) . \]
\[\left( - 3, \infty \right) \cap \left( - \infty , 7 \right) = \left( - 3, 7 \right)\]
\[ \therefore x \in \left( - 3, 7 \right)\]
\[\text{ Thus, thesolution of the given set of inequalities is } \left( - 3, 7 \right) .\] 

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 15 Linear Inequations
Exercise 15.2 | Q 2 | Page 10
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