Question

Solve the compound inequality: 3x + 6 < 12 AND 6x + 24 < 12

Answer 1

Answer:

$x < -2$.

Step-by-step explanation:

It is given that $3x + 6 < 12$ and $6x + 24 < 12$.

For $3x + 6 < 12$,

$3x < 12-6$

$3x < 6$

Divide both sides by 2.

$x < 2$      ...(i)

For $6x + 24 < 12$,

$6x< 12-24$

$6x< -12$

Divide both sides by 6.

$x < -2$      ...(ii)

From (i) and (ii), we get

$x < 2\text{ and }x<-2$

$\Rightarrow x<-2$

Therefore, the required answer is $x < -2$.