Solution:|x -5| =2 x -5=( ) or x -5 =( ) x = 2 +( ) or x = ( )+5 x = ( )or x=( )
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Given, 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}
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