Solve the following system of equations in R.

$2 x - 7 > 5 - x, 11 - 5 x \leq 1$

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Solution

Consider the first inequation,

$2 x - 7 > 5 - x \Rightarrow 2 x + x > 5 + 7 \Rightarrow 3 x > 12 \Rightarrow x > \frac{12}{3} \Rightarrow x > 4 . . . (i) C o n s i d e r t h e s e c o n d i n e q u a t i o n, 11 - 5 x \leq 1 \Rightarrow - 5 x \leq 1 - 11 \Rightarrow - 5 x \leq - 10 \Rightarrow 5 x \geq 10 \Rightarrow x \geq 2 . . . (i i) From (i) and (ii), (4, \infty) is the solution set of the simultaneous equations.$

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