Solve the system of equations in R.5x – 1 < 24, 5x + 1 > –24

1.	Solve the system of equations in R.5x – 1 < 24, 5x + 1 > –24
Answer» Given as 5x – 1 < 24 and 5x + 1 > –24 Now, let us consider the first inequality. 5x – 1 < 24 5x – 1 + 1 < 24 + 1 5x < 25 Dividing both the sides by 5 we get, 5x/5 < 25/5 x < 5 ∴ x ∈ (–∞, 5)… (1) Then, let us consider the second inequality. 5x + 1 > –24 5x + 1 – 1 > –24 – 1 5x > –25 Dividing both the sides by 5 we get, 5x/5 > -25/5 x > -5 ∴ x ∈ (–5, ∞)… (2) From (1) and (2), we get x ∈ (–∞, 5) ∩ (–5, ∞) x ∈ (–5, 5) Hence, the solution of the given system of inequations is (–5, 5).

Answer»

Given as

5x – 1 < 24 and 5x + 1 > –24

Now, let us consider the first inequality.

5x – 1 < 24

5x – 1 + 1 < 24 + 1

5x < 25

Dividing both the sides by 5 we get,

5x/5 < 25/5

x < 5

∴ x ∈ (–∞, 5)… (1)

Then, let us consider the second inequality.

5x + 1 > –24

5x + 1 – 1 > –24 – 1

5x > –25

Dividing both the sides by 5 we get,

5x/5 > -25/5

x > -5

∴ x ∈ (–5, ∞)… (2)

From (1) and (2), we get

x ∈ (–∞, 5) ∩ (–5, ∞)

x ∈ (–5, 5)

Hence, the solution of the given system of inequations is (–5, 5).

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