Q. 194.0( 2 Votes )

Solve each of the

Answer :

Given 10 ≤ –5(x – 2) < 20


The above inequality can be split into two inequalities.


10 ≤ –5(x – 2) and –5(x – 2) < 20


Let us consider the first inequality.


10 ≤ –5(x – 2)


10 ≤ –5x + 10


10 – 10 ≤ –5x + 10 – 10


0 ≤ –5x


0 + 5x ≤ –5x + 5x


5x ≤ 0


x ≤ 0


x (–∞, 0] (1)


Now, let us consider the second inequality.


–5(x – 2) < 20


–5x + 10 < 20


–5x + 10 – 10 < 20 – 10


–5x < 10



–x < 2


x > –2


x (–2, ∞) (2)


From (1) and (2), we get


x (–∞, 0] (–2, ∞)


x (–2, 0]


Thus, the solution of the given system of inequations is (–2, 0].


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