Q. 104.2( 5 Votes )
Solve each of the following system of inequations in R
11 – 5x > –4, 4x + 13 ≤ –11
Answer :
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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