Solve the linear inequations in R.11 – 5x > –4, 4x + 13 ≤ –11

1.	Solve the linear inequations in R.11 – 5x > –4, 4x + 13 ≤ –11
Answer» Given as 11 – 5x > –4 and 4x + 13 ≤ –11 Now, let us consider the first inequality. 11 – 5x > –4 11 – 5x – 11 > –4 – 11 –5x > –15 Dividing both the sides by 5 we get, -5x/5 > -15/5 –x > –3 x < 3 ∴ x ∈ (–∞, 3) (1) Then, let us consider the second inequality. 4x + 13 ≤ –11 4x + 13 – 13 ≤ –11 – 13 4x ≤ –24 Dividing both the sides by 4 we get, 4x/4 ≤ –24/4 x ≤ –6 ∴ x ∈ (–∞, –6] (2) From (1) and (2), we get x ∈ (–∞, 3) ∩ (–∞, –6] x ∈ (–∞, –6] Hence, the solution of the given system of inequations is (–∞, –6].

Answer»

Given as

11 – 5x > –4 and 4x + 13 ≤ –11

Now, let us consider the first inequality.

11 – 5x > –4

11 – 5x – 11 > –4 – 11

–5x > –15

Dividing both the sides by 5 we get,

-5x/5 > -15/5
–x > –3

x < 3

∴ x ∈ (–∞, 3) (1)

Then, let us consider the second inequality.

4x + 13 ≤ –11

4x + 13 – 13 ≤ –11 – 13

4x ≤ –24

Dividing both the sides by 4 we get,

4x/4 ≤ –24/4

x ≤ –6

∴ x ∈ (–∞, –6] (2)

From (1) and (2), we get

x ∈ (–∞, 3) ∩ (–∞, –6]

x ∈ (–∞, –6]

Hence, the solution of the given system of inequations is (–∞, –6].

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