Solve each of the following system of inequations in R

11 – 5x > –4, 4x + 13 ≤ –11

Given 11 – 5x > –4 and 4x + 13 ≤ –11


Let us consider the first inequality.


11 – 5x > –4


11 – 5x – 11 > –4 – 11


–5x > –15



–x > –3


x < 3


x (–∞, 3) (1)


Now, let us consider the second inequality.


4x + 13 ≤ –11


4x + 13 – 13 ≤ –11 – 13


4x ≤ –24



x ≤ –6


x (–∞, –6] (2)


From (1) and (2), we get


x (–∞, 3) (–∞, –6]


x (–∞, –6]


Thus, the solution of the given system of inequations is (–∞, –6].


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