Mathematics
If x ∈ N, find the solution set of inequations.
(i) 5x + 3 ≤ 2x + 18
(ii) 3x - 2 < 19 - 4x
Linear Inequations
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Answer
(i) 5x + 3 ≤ 2x + 18
⇒ 5x - 2x ≤ 18 - 3
⇒ 3x ≤ 15
Dividing both sides by 3
⇒ x ≤ 5
Since, x ∈ N
∴ Solution set = {1, 2, 3, 4, 5}.
(ii) 3x - 2 < 19 - 4x
⇒ 3x + 4x < 19 + 2
⇒ 7x < 21
Dividing both sides by 7 we get,
⇒ x < 3
Since, x ∈ N
∴ Solution set = {1, 2}.
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Case study :
A teacher asked to Rohan to draw a triangle with following condition: The longest side of the triangle is 7 cm less than twice the shortest side and third side is 7 cm shorter than longest side. The perimeter of the triangle is atleast 84 cm.
Based on the above information, form a linear inequation and answer the following questions :
(i) What is the minimum length of the shortest side ?
(ii) What is the minimum length of the longest side ?
(iii) Identify the type of triangle that Rohan has drawn along with the length possible sides he got.
(iv) What is the least area of the triangle drawn ?