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प्रश्न
Solve each of the following system of equations in R.
2x − 7 > 5 − x, 11 − 5x ≤ 1
उत्तर
Given as
2x – 7 > 5 – x and 11 – 5x ≤ 1
Now, let us consider the first inequality.
2x – 7 > 5 – x
2x – 7 + 7 > 5 – x + 7
2x > 12 – x
2x + x > 12 – x + x
3x > 12
Dividing both the sides by 3 we get,
`(3x)/3 > 12/3`
x > 4
∴ x ∈ (4, ∞) ...(1)
Then, let us consider the second inequality.
11 – 5x ≤ 1
11 – 5x – 11 ≤ 1 – 11
– 5x ≤ – 10
Dividing both the sides by 5 we get,
`(– 5x)/5 ≤ (–10)/5`
–x ≤ –2
x ≥ 2
∴ x ∈ (2, ∞) ...(2)
From (1) and (2) we get
x ∈ (4, ∞) ∩ (2, ∞)
x ∈ (4, ∞)
Hence, the solution of the given system of inequations is (4, ∞).
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