Book: RD Sharma - Mathematics
Chapter: 15. Linear Inequations
Subject: Maths - Class 11th
Q. No. 19 of Exercise 15.2
Listen NCERT Audio Books to boost your productivity and retention power by 2X.
19
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].
