Question

3 ≤ 2x-1 ≤ 5 , x € I​

Answer 1

Step-by-step explanation:

P={x : 5<2x−1≤11,x∈R} and Q={x : −1≤3+4x<23,x∈I}

Solving for P,

5<2x−1≤11

⇒5+1<2x≤11+1

⇒6<2x≤12

⇒3<x≤6

Hence, P={x : 3<x≤6,x∈R}

The solution P is represented on number line (a).

Next, solving for Q

−⇒1≤3+4x<23

⇒−1−3≤4x<23−3

⇒−4≤4x<20

⇒−1≤x<5

As Q∈I

Hence, solution Q={−1,0,1,2,3,4}

The solution Q is represented on number line (b).

Therefore, P∩Q={4}