Question

Given
$P=\{x:6<3x-9<12,x\in R\}Q=\{x:-1\le 3+4x\le 35,x\in I\}$
Write down the elements of $P\cap Q$

• A. {-1,0,1,2,3,4,5,6,7,8}
• B. {-1,0,1,2,3}
• C. {6}
• D. {5}

Answer 1

The correct option is C

{6}

For P
3x -9 > 6
3x > 9+6
3x > 15
$x>\frac{15}{3}$
x >5 ............(1)
3x -9 < 12
3x < 21
x < 7..............(2)
On combining equation (1) & (2), We get the solution set P =(5, 7)
For Q

$4x+3\ge -1$
$4x\ge -1-3$
$x\ge \frac{-4}{4}$
$x\ge -1$

And
$4x+3\le 35$
$4x\le 32$
$x\le \frac{32}{4}$
$x\le 8$

$\therefore$ The solution set is {-1,0,1,2,3,4,5,6,7,8}
$P\cap Q=6$