Mathematics
Solve and graph the solution set of :
5 > p - 1 > 2 or 7 ≤ 2p - 1 ≤ 17; p ∈ R
Linear Inequations
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Answer
Given,
5 > p - 1 > 2 or 7 ≤ 2p - 1 ≤ 17
Solving, 5 > p - 1 > 2
Solving, L.H.S. of the inequation we get,
⇒ 5 > p - 1
⇒ p < 5 + 1
⇒ p < 6 ……(i)
Solving, R.H.S. of the inequation we get,
⇒ p - 1 > 2
⇒ p > 2 + 1
⇒ p > 3 …..(ii)
From (i) and (ii) we get,
⇒ 3 < p < 6
Solving, 7 ≤ 2p - 1 ≤ 17
Solving, L.H.S. of the inequation we get,
⇒ 7 ≤ 2p - 1
⇒ 2p ≥ 7 + 1
⇒ 2p ≥ 8
⇒ p ≥ 4 ……(iii)
Solving, R.H.S. of the inequation we get,
⇒ 2p - 1 ≤ 17
⇒ 2p ≤ 18
⇒ p ≤ 9 ……(iv)
From (iii) and (iv) we get,
⇒ 4 ≤ p ≤ 9.
So, we can say,
3 < p < 6 or 4 ≤ p ≤ 9.
⇒ 3 < p ≤ 9.
Hence, 3 < p ≤ 9.
Solution on the number line is :
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