Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
Advertisement Remove all ads

Solve Each of the Following System of Equations in R. X + 5 > 2(X + 1), 2 − X < 3 (X + 2) - Mathematics

Solve each of the following system of equations in R. 

 x + 5 > 2(x + 1), 2 − x < 3 (x + 2) 

Advertisement Remove all ads

Solution

\[\text{ We have }, 4x - 1 \leq 0\]
\[ \Rightarrow 4x \leq 1\]
\[ \Rightarrow x \leq \frac{1}{4} (\text{ Dividing both the sides by } 4)\]
\[ \Rightarrow x \in ( - \infty , \frac{1}{4}] . . . (i)\]
\[\text{ Also }, 3 - 4x < 0\]
\[ \Rightarrow 0 > 3 - 4x\]
\[ \Rightarrow 4x > 3\]
\[ \Rightarrow x > \frac{3}{4} \text{ Dividing both sides by 4 }\]
\[ \Rightarrow x \in \left( \frac{3}{4}, \infty \right) . . . (ii)\]
\[\text{ Hence, the solution of the given set of inequalities is the intersection of } (i) \text{ and } (ii) . \]
\[But, \left( - \infty \frac{1}{4} \right) \cap \left( \frac{3}{4}, \infty \right) = \phi\]
\[\text{ Thus, the given set of inequations has no solution } .\] 

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 15 Linear Inequations
Exercise 15.2 | Q 12 | Page 15
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×