Listen NCERT Audio Books to boost your productivity and retention power by 2X.
Solve each of the following system of inequations in R
10 ≤ –5(x – 2) < 20
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].