tmua 2017 Q5

tmua · Uk · paper1 1 marks Inequalities Simultaneous/Compound Quadratic Inequalities
$S$ is the complete set of values of $x$ which satisfy both the inequalities
$$x ^ { 2 } - 8 x + 12 < 0 \text { and } 2 x + 1 > 9$$
The set $S$ can also be represented as a single inequality.
Which one of the following single inequalities represents the set $S$ ?
A $\left( x ^ { 2 } - 8 x + 12 \right) ( 2 x + 1 ) < 0$
B $\left( x ^ { 2 } - 8 x + 12 \right) ( 2 x + 1 ) > 0$
C $x ^ { 2 } - 10 x + 24 < 0$
D $x ^ { 2 } - 10 x + 24 > 0$
E $\quad x ^ { 2 } - 6 x + 8 < 0$
F $\quad x ^ { 2 } - 6 x + 8 > 0$
G $x < 2$
H $x > 6$
& C
$S$ is the complete set of values of $x$ which satisfy both the inequalities

$$x ^ { 2 } - 8 x + 12 < 0 \text { and } 2 x + 1 > 9$$

The set $S$ can also be represented as a single inequality.

Which one of the following single inequalities represents the set $S$ ?

A $\left( x ^ { 2 } - 8 x + 12 \right) ( 2 x + 1 ) < 0$

B $\left( x ^ { 2 } - 8 x + 12 \right) ( 2 x + 1 ) > 0$

C $x ^ { 2 } - 10 x + 24 < 0$

D $x ^ { 2 } - 10 x + 24 > 0$

E $\quad x ^ { 2 } - 6 x + 8 < 0$

F $\quad x ^ { 2 } - 6 x + 8 > 0$

G $x < 2$

H $x > 6$