Solve and graph the solution set of :

5 > p - 1 > 2 or 7 ≤ 2p - 1 ≤ 17; p ∈ R

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 :