Question

) Given P={ x: 5 < 2x – 1 ≤ 11, x ∈ R } and Q= { x : -1 ≤ 3 + 4x < 23, x ∈ I }. Find P and Q.

Draw number line to show :

i) P’ ∩ Q

ii) P ∩ Q ​

Answer 1

Answer:

$5 < 2x - 1 \leqslant 11$

$6 < 2x \leqslant 12$

$3 < x \leqslant 6$

so P = ( 3 , 6 ]

now,

$- 1 \leqslant 3 + 4x < 23$

$- 4 \leqslant 4x < 20$

$- 1 \leqslant x < 5$

x€ I then X = -1,0,1,2,3,4

so Q = { -1, 0, 1, 2, 3, 4 }