Question

Solve each of the following system of equations in R. 

2 (x − 6) < 3x − 7, 11 − 2x < 6 − x 

Answer 1

\[2\left( x - 6 \right) < 3x - 7\]
\[ \Rightarrow 2x - 12 < 3x - 7\]
\[ \Rightarrow 3x - 7 > 2x - 12\]
\[ \Rightarrow 3x - 2x > - 12 + 7\]
\[ \Rightarrow x > - 5\]
\[ \Rightarrow x \in \left( - 5, \infty \right) . . . (i)\]
\[\text{ Also }, 11 - 2x < 6 - x\]
\[ \Rightarrow 6 - x > 11 - 2x\]
\[ \Rightarrow 2x - x > 11 - 6\]
\[ \Rightarrow x > 5\]
\[ \Rightarrow x \in \left( 5, \infty \right) . . . (ii)\]
\[\text{Hence, the solution of the given inequation is the intersection of } (i) \text{ and } (ii) . \]
\[\left( - 5, \infty \right) \cap \left( 5, \infty \right) = \left( 5, \infty \right)\]
\[\text{ Hence, the solution of the given inequation is } \left( 5, \infty \right) .\]