 ## Book: RD Sharma - Mathematics

### Chapter: 15. Linear Inequations

#### Subject: Maths - Class 11th

##### Q. No. 19 of Exercise 15.2

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19
##### Solve each of the following system of inequations in R10 ≤ –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].

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