Solve the following system of equations in R.

$2 (x - 6) < 3 x - 7, 11 - 2 x < 6 - x$

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Solution

Consider the first inequation,

$2 (x - 6) < 3 x - 7 \Rightarrow 2 x - 12 < 3 x - 7 \Rightarrow - 5 < x . . . (i)$

Consider the second inequation,

$11 - 2 x < 6 - x - 2 x + x < 6 - 11 - x < - 5 x > 5 . . . (i i)$

From (i) and (ii), $(5, \infty)$ is the solution set of the simultaneous equations.

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